The core idea is deceptively simple. Instead of solving the partial differential equations that govern fluid flow, heat transfer, or atmospheric dynamics from scratch every time, a foundation model is trained on vast libraries of existing simulation data. Once trained, it can produce predictions in minutes that would otherwise demand days of number-crunching. The authors describe these systems as reusable base models: rather than starting over for each new application, scientists can adapt a pre-trained model to tasks such as inverse design—working backward from a desired outcome to find the parameters that produce it—or uncertainty quantification, without retraining from zero. The result is a workflow in which rapid, physics-informed optimization cycles become routine rather than exceptional.

The article is careful to position foundation models as complements rather than replacements for traditional simulation. The authors draw a direct line to older engineering practice: reduced-order and surrogate models, such as Reynolds-averaged approaches in fluid dynamics, have long been used to trade some physical fidelity for enormous gains in speed. Foundation models share that motivation but bring far greater expressive power, learning from large collections of simulation and experimental data using architectures like transformers and graph neural networks. The authors emphasize that these systems support high-throughput virtual experimentation and help researchers navigate design tradeoffs, while expert judgment and full-fidelity solvers remain essential anchors of the workflow.

The evidence for this approach spans multiple domains. In Earth system science, models such as DeepMind’s GraphCast and NVIDIA’s FourCastNet already use large spatiotemporal datasets to improve weather and climate prediction while providing actionable guidance to human forecasters. In materials science, models trained on crystal structure databases help researchers prioritize promising candidates for further study. Drug discovery efforts use similar techniques for protein structure prediction and molecular design. In fusion energy research, data-driven models assist physicists with plasma control and scenario planning in operational environments that are too complex for intuition alone. The common thread is that foundation models learn intricate physical and chemical relationships from diverse data, enabling rapid prediction across a broad range of physical domains.

One of the article’s most technically grounded sections concerns data management, an often-overlooked foundation of the entire enterprise. The authors argue that as foundation models scale to production on high-performance computing systems, the quality and organization of training data becomes the decisive factor in achieving both speed and generalization. Building high-quality datasets requires programmatic pipelines for collection, quality control, de-duplication, consistent labeling, and machine-readable provenance. They advocate moving beyond generic FAIR data principles toward a campaign-oriented governance model, in which simulation campaigns are recorded with standardized workflows and ontologies, and data curation is driven by impact metrics such as time-to-insight and downstream model quality rather than raw storage volume.

At exascale, the authors note, storing every high-order field produced by a simulation is simply infeasible, making compression a first-class design choice rather than an afterthought. Modern error-bounded lossy compression methods can dramatically reduce data footprints, but the authors insist that fidelity must be defined by physics-aware criteria—controlling errors in energy or gradients, for example—and by quantifying how compression perturbations affect downstream surrogates and emulators. Integrated in situ or in transit within the simulation pipeline, compression can even act as a learnable encoder, yielding compact features that minimize input-output and memory demands during pre-training and fine-tuning while maintaining strict error controls for diagnostics.

To make scientific data usable across domains, the authors propose a token-centric view of AI-readiness that mirrors how foundation models themselves process information. Descriptor tokens would capture meshes, coordinates, units, and provenance, while feature tokens represent compressed field content. Fusion mechanisms would bind these tokens across simulations, experiments, and modalities into coherent scientific narratives. Anchoring such tokens in community standards—netCDF-like schemas for Earth system modeling, for instance—would give model teams a stable, extensible interface to simulation data, creating a feedback loop from simulation to model training and back again.

On the architectural side, the article distinguishes between two main families of models suited to scientific simulation. For regular grids such as latitude-longitude climate meshes, Vision Transformer-style encoders use patch embeddings that align naturally with GPU tensor cores and batched input-output operations, facilitating large-scale spatial correlations with predictable memory layouts. For spherical or unstructured domains, graph neural networks encode locality and adjacency through message passing, preserving mesh topology without expensive remeshing. Temporal structure is typically handled by autoregressive or time-conditioned transformers, though the authors caution that long temporal windows significantly increase attention memory, communication overhead, and checkpoint sizes—all key bottlenecks on distributed supercomputing systems.

Two design principles run through the article’s architectural recommendations. First, physics-aware inductive biases—constraints that force models to respect invariants, conservation laws, and symmetries—improve data efficiency and reliability across different physical regimes. Second, token- and compute-adaptivity allows cost to scale with solution complexity rather than nominal grid size, using mechanisms such as windowed or hierarchical attention for long-range dependencies, sparsity and mixture-of-experts routing for conditional computation, and adaptive token pruning that focuses model capacity where dynamics are actually active. Linear or subquadratic attention variants further reduce the quadratic growth of standard self-attention, enabling extreme resolutions on modern accelerators.

The article also details concrete parallelization strategies drawn from ORBIT-class efforts at Oak Ridge, identifying four key levers for scaling Vision Transformer-based foundation models on supercomputers. Linear-complexity attention reduces self-attention cost from quadratic to linear, enabling multi-billion-token contexts at high resolution. Hybrid parallelization—combining tensor and model sharding with data parallelism—scales to models with over 100 billion parameters while controlling communication and memory overhead. Lightweight architectural efficiency improves hardware utilization without sacrificing accuracy, and domain specialization with robust uncertainty quantification maintains physical consistency in multi-variable predictions. The authors acknowledge that these techniques trade exact global attention for sparse routing and introduce modest auxiliary indices and buffers, and they stress that accuracy-cost impacts must be evaluated explicitly rather than assumed away.

Looking beyond transformers, the article highlights an emerging alternative: pairing diffusion-based generative models with state-space architectures such as Mamba to target linear-time complexity and lower GPU memory requirements. Mapping one-dimensional Mamba architectures to two- and three-dimensional scientific fields uses multi-directional and zigzag scanning patterns, while hybrid designs retain a small fraction of self-attention to preserve global coherence. These approaches reduce activation and key-value cache traffic, ease pressure on interconnects, and enable longer contexts on fixed high-bandwidth memory budgets—naturally improving the scalability of diffusion-based foundation models for probabilistic forecasting, ensemble generation, and uncertainty quantification in chaotic systems.

Performance on supercomputers, the authors observe, is often limited more by memory capacity, memory bandwidth, and collective communication than by raw floating-point throughput. Training costs for multi-channel two- and three-dimensional fields over long contexts are dominated by activation and key-value cache residency, optimizer state footprints, tensor layout conversions, and synchronization overhead. To address this, the article catalogs a battery of optimization techniques: fused attention kernels that reduce high-bandwidth memory movement, hybrid parallelism that shards parameters, gradients, and optimizer states across devices, key-value cache management strategies such as PagedAttention that improve batching efficiency during inference, and topology-aware placement combined with tensor fusion and overlapping collectives that convert theoretical peak performance into sustained throughput.

Cross-layer co-design emerges as a unifying theme. Sequence parallelism and tiling constrain activation footprints; activation checkpointing trades computation for memory; gradient accumulation increases effective batch size; and conditional computation through sparse activations and mixture-of-experts scales cost with solution complexity. Reliability receives particular attention: mixed and low-precision training requires careful gradient scaling and clipping for numerical stability, while deterministic kernels support fast recovery and reproducibility. HPC-native task-based runtimes such as PaRSEC orchestrate workflows as dependency graphs, overlapping collective communication with computation and prioritizing latency-critical inference alongside throughput-driven training.

The article closes with a discussion of trust, arguing that adoption ultimately depends on rigorous validation. The authors call for comparing foundation model outputs against traditional numerical solvers and observed data, quantifying uncertainty through ensembles or diffusion techniques, and enforcing physical constraints. They propose a standardized evaluation framework incorporating accuracy, efficiency, and trustworthiness metrics—mirroring the verification, physics consistency checks, and cross-solver benchmarking with confidence intervals already standard in numerical simulation—alongside a hardware-aware simulation platform for evaluating pipelines across computational architectures with pre-registered acceptance thresholds. Understanding the tradeoff between accuracy and computational time, they conclude, will let practitioners allocate resources effectively and make informed decisions about when foundation models can deliver swift, credible scientific insight on production supercomputers.

Subject of Research: Scalable foundation models for accelerating numerical simulations on high-performance computing platforms

Article Title: Scalable foundation models for numerical simulations on HPC platforms

Article References: Wang, D., Gong, Q., Liu, Z., Wang, X., Cao, Q., & Klasky, S. (2026). Scalable foundation models for numerical simulations on HPC platforms. Frontiers in High Performance Computing, 4, Article 1778471. https://doi.org/10.3389/fhpcp.2026.1778471

Image Credits: AI Generated

DOI: 10.3389/fhpcp.2026.1778471

Keywords: foundation models, high-performance computing, numerical simulation, exascale computing, Vision Transformer, graph neural networks, diffusion models, lossy compression, AI-ready data, uncertainty quantification, parallelization, scientific machine learning

John George Francis and Anil Shaji focused on transmon qubits, the workhorse of IBM’s quantum processors and many other superconducting platforms. Transmons are engineered from Josephson junctions and superconducting circuits to be relatively insensitive to charge noise, a design choice that has made them the most widely deployed qubit technology in the world. Yet even the best-fabricated transmons deviate from the idealized textbook description. Stray couplings, higher energy levels, and control imperfections all conspire to make the actual dynamics of the system richer and messier than the standard Hamiltonian predicts.

The team targeted one of the most important operations in the superconducting quantum computing repertoire: the cross-resonance gate. In this scheme, microwaves are applied to a target qubit at the frequency of its control qubit neighbor, creating an entangling interaction that serves as a fundamental building block for two-qubit logic. The cross-resonance interaction has a well-known effective Hamiltonian description, developed in earlier theoretical work, but that description is itself an approximation whose accuracy depends on the details of the hardware and the drive parameters. When the idealized model is used to predict what a real gate does, errors accumulate quickly.

To quantify those errors and correct them, Francis and Shaji turned to real experimental data from ibm_kyiv, one of the processors accessible on the IBM Quantum cloud platform. They collected measurement outcomes for two transmon qubits driven by microwave pulses of varying amplitudes and evolution times, spanning a range of operating conditions. Each data point captured the probabilities of the different computational basis states after the system evolved under the cross-resonance drive, providing a rich empirical fingerprint of the true dynamics that no purely theoretical model could be expected to reproduce exactly.

The heart of their method is a correction operator added to the standard Hamiltonian. Rather than guessing the correction from first principles, the researchers wrote down an ansatz, a flexible mathematical form whose matrix elements are free parameters to be optimized. The goal of the optimization is simple to state and hard to achieve: find the correction terms that make the corrected Hamiltonian’s predicted evolution match the observed hardware data as closely as possible across all the measured amplitudes and times. Because the ansatz is not unique, different parameter choices can yield equally good fits, so the team developed methods to characterize an entire equivalence class of effective corrections rather than a single answer.

Optimizing parameters inside a differential equation is exactly the kind of problem that scientific machine learning was built to solve. The researchers employed adjoint sensitivity analysis, a technique that efficiently computes how the final outcome of a dynamical simulation changes with respect to every parameter in the model, without the prohibitive cost of naive approaches. Combined with gradient descent, this allowed the correction terms to be tuned iteratively until the simulated and measured probability distributions converged. The approach draws on the framework of universal differential equations, in which physical models are embedded in differentiable programs that machine learning tools can optimize end to end.

The results are striking. With the uncorrected Hamiltonian, the worst-case average absolute error in predicting the final measurement probabilities reached 0.48, meaning the theoretical model could be wrong by nearly half a full probability unit, a level of disagreement that would render any gate calibration based on the model unreliable. After the data-driven correction was applied, that worst-case error dropped below 0.05, an improvement of nearly a factor of ten. The corrected Hamiltonian tracked the survival probabilities of all four initial two-qubit states across the full range of pulse amplitudes tested, reproducing the fine structure of the hardware’s time evolution that the standard model missed entirely.

Why does this matter beyond one pair of qubits on one machine? Gate fidelities in today’s quantum processors are limited not only by decoherence but by systematic modeling errors, and as the field marches toward error-corrected, fault-tolerant machines, every fraction of a percent of gate accuracy counts. Accurate Hamiltonian models are also the foundation of optimal control techniques, which design pulse sequences to implement gates as faithfully as possible. If the underlying model is wrong, even the most sophisticated pulse optimization will steer the quantum system to the wrong destination. A data-driven correction loop, in which the model continuously learns from the hardware it describes, offers a path to calibrations that stay faithful as devices drift and age.

The work also highlights a broader shift in how quantum engineers think about the relationship between theory and experiment. Traditional approaches either derive effective Hamiltonians perturbatively from circuit theory or fit a handful of parameters to targeted experiments. The scientific machine learning approach is more ambitious: it treats the Hamiltonian itself as a learnable object, constrained by physics but refined by data, and it embraces the fact that multiple effective descriptions may be equally valid. That equivalence-class perspective is philosophically interesting, but it is also practically useful, because it tells engineers which features of a correction are physically meaningful and which are artifacts of a particular parameterization.

Francis and Shaji’s study, published in Quantum Information Processing, was supported in part by India’s National Quantum Mission and used the high-performance computing facilities at IISER Thiruvananthapuram. The underlying data have been made openly available, allowing other groups to test and extend the method on different hardware platforms. As quantum processors scale to hundreds and eventually thousands of qubits, manual calibration of every interaction will become impossible, and techniques like this one, which let the machine teach itself the physics of its own imperfections, may become as essential to quantum computing as the qubits themselves.

Subject of Research: Data-driven correction of the cross-resonance Hamiltonian of transmon qubits using scientific machine learning

Article Title: Data-driven Hamiltonian correction of transmon qubits

Article References: Francis, J. G., & Shaji, A. (2026). Data-driven Hamiltonian correction of transmon qubits. Quantum Information Processing, 25(10), Article 328. https://doi.org/10.1007/s11128-026-05350-7

Image Credits: AI Generated

DOI: 10.1007/s11128-026-05350-7

Keywords: transmon qubits, Hamiltonian correction, cross-resonance gate, scientific machine learning, IBM Quantum, quantum computing, gradient descent, adjoint sensitivity, quantum control, superconducting qubits, gate fidelity, quantum information processing

The review, led by Mohammad Nooraiepour of the University of Oslo with colleagues from the University of Bergen, Siemens Energy AI Lab, and Friedrich-Schiller-University Jena, does not declare a winner in the contest between traditional solvers and neural networks. Instead, it delivers a more unsettling and more useful conclusion: the two paradigms are epistemologically different kinds of machinery, and confusing them leads to both overhyped claims about artificial intelligence and underuse of what it genuinely offers. Classical methods are deductive, meaning their errors can be bounded by quantities derived directly from the structure of the equation and the parameters of the discretization. Machine learning methods are inductive, meaning their accuracy depends on statistical proximity to the data they were trained on. That single distinction, the authors argue, determines not which approach is superior but what each can certify, and therefore where each should be deployed.

To make the comparison rigorous, the review organizes the entire field around six fundamental computational challenges: high dimensionality, nonlinearity, geometric complexity, discontinuities, multiscale phenomena, and multiphysics coupling. These six axes function as a common testing ground. Classical methods, including finite difference, finite element, finite volume, and spectral discretizations, are assessed on each axis for their structure-preserving properties, their rigorous convergence theory, and their scalable solver design. The verdict is nuanced. On problems of moderate dimension with well-behaved geometry, classical methods remain unmatched, delivering certified accuracy with error estimates that engineers can take to a regulator or a certification authority. But the review is candid about their persistent weaknesses: the curse of dimensionality crushes grid-based methods as the number of variables grows, and geometrically complex domains can make mesh generation a bottleneck that consumes more human effort than the solve itself.

Machine learning approaches are then subjected to exactly the same critical assessment, which is itself a departure from much of the existing literature, where neural methods are typically benchmarked only against other neural methods. The review builds a taxonomy organized by the degree to which physical knowledge is incorporated into the learning process. At one end sit purely data-driven surrogates; in the middle sit physics-informed neural networks, which embed the residual of the governing PDE directly into the loss function so that the network is penalized for violating the physics; and further along sit neural operators, which learn mappings between function spaces rather than pointwise values, promising generalization across families of related problems. Graph-based architectures, transformers, and generative models round out the landscape, alongside hybrid frameworks that interleave classical solvers with learned components.

The critical findings here are sobering for anyone hoping that neural networks will simply replace finite element solvers. Physics-informed neural networks, despite enormous popularity, struggle with stiff problems, sharp gradients, and the kind of discontinuous behavior that dominates real multiphysics applications such as fracture propagation or salt precipitation during carbon dioxide storage. Their training is often fragile, their convergence theory is far less mature, and their accuracy guarantees are fundamentally statistical rather than deterministic. Neural operators fare better on generalization across parameter ranges, but the review emphasizes that their reliability is always conditional on the training distribution. A neural surrogate that performs beautifully within the range of parameters it has seen can fail catastrophically, and silently, the moment it is asked to extrapolate. Classical methods never fail silently in quite the same way, because their error bounds degrade predictably with refinement.

What elevates the review above a simple scorecard is its treatment of complementarity. The authors identify three genuine synergies between the paradigms. First, machine learning can accelerate the inner workings of classical solvers, for example by learning preconditioners, coarse-grid corrections, or adaptive mesh indicators, while the outer classical framework retains its convergence guarantees. Second, classical methods can generate the high-fidelity training data and validation benchmarks that neural surrogates require, creating a pipeline in which the deductive method certifies the inductive one. Third, learned models can capture constitutive behavior or subgrid physics that is too expensive or too poorly understood to resolve explicitly, feeding these closures into structure-preserving classical schemes. In each case, the division of labor follows the epistemological split: the learned component supplies speed and flexibility where statistics suffice, and the classical component supplies certification where proof is required.

The review goes further and develops design principles for hybrid methods, including a framework for what the authors call the structure inheritance problem, that is, how to ensure that a learned component does not destroy the conservation laws, stability properties, or symmetry structures that a classical discretization was carefully constructed to preserve. They also propose an error budget decomposition that separates the total error of a hybrid simulation into three contributions: the discretization error of the classical scheme, the approximation error of the neural component, and the coupling error introduced at their interface. This decomposition matters because it turns hybrid design from an art into an accounting exercise. If a coupled simulation goes wrong, the framework tells practitioners where to look, and it prevents the common failure mode in which a neural component’s unquantified error is silently absorbed into an apparently converged classical result.

Looking forward, the authors assess emerging frontiers with the same skeptical lens. Foundation models for scientific computing, inspired by the large language models that transformed natural language processing, are evaluated against the structural constraints of PDE solving, and the review asks whether the scaling laws that powered language models can plausibly transfer to problems governed by conservation laws and boundary conditions. Differentiable programming for inverse design, in which entire simulation pipelines are made end-to-end differentiable so that gradients can flow from design objectives back through the solver, is judged promising but dependent on the same error-accounting discipline. Quantum algorithms for PDEs are treated with particular caution: the review distinguishes between barriers that are fundamental and those that are merely contingent on engineering progress, and finds that for several quantum approaches the current obstacles look structural rather than incidental. Exascale co-design, the joint development of algorithms and hardware at extreme scale, is identified as a domain where hybrid classical-learned solvers may find their most immediate practical impact.

The timing of this synthesis is significant. Scientific machine learning has grown from a niche curiosity into a field with its own conferences, journals, and funding programs, and the hype cycle has produced both genuine breakthroughs and inflated claims. Reviews that merely catalog methods multiply yearly, but rigorous evaluations that apply identical criteria to both paradigms remain rare. By insisting that epistemological character, rather than computational speed, is the primary criterion for responsible method selection, the review provides something the community has lacked: a principled basis for deciding, problem by problem, whether a learned surrogate, a certified classical solver, or a carefully engineered hybrid is the right tool. The stakes are concrete. Applications such as geological carbon storage, where the authors’ own research is anchored through projects on salt precipitation and convective mixing during CO2 injection, demand simulations that are simultaneously fast enough for uncertainty quantification over thousands of realizations and trustworthy enough to inform regulatory decisions about subsurface storage integrity.

The conclusion the authors reach is not that one paradigm supersedes the other, but that their principled integration offers the most credible path toward computationally tractable solutions to the most consequential open problems that neither approach can address alone. For decades, computational science advanced by refining discretizations, solvers, and hardware within a single deductive tradition. The last several years added a second tradition with fundamentally different guarantees. The review’s lasting contribution may be its refusal to choose between them, and its demonstration that the future of simulation lies in knowing precisely what each tradition can promise, what it cannot, and how to combine them without letting the strengths of one conceal the weaknesses of the other. In an era when artificial intelligence is routinely described as a replacement for existing tools, this is a refreshingly precise message: the equations that govern the physical world will be solved not by machines alone, nor by classical mathematics alone, but by an alliance whose terms are now, finally, being written down.

Subject of Research: A critical synthesis of classical numerical, machine learning, and hybrid methods for solving partial differential equations

Article Title: Partial differential equations in the age of machine learning: a critical synthesis of classical, machine learning, and hybrid methods

Article References: Nooraiepour, M., Both, J. W., Kadeethum, T., & Sadeghnejad, S. (2026). Partial differential equations in the age of machine learning: a critical synthesis of classical, machine learning, and hybrid methods. Artificial Intelligence Review. https://doi.org/10.1007/s10462-026-11677-5

Image Credits: AI Generated

DOI: 10.1007/s10462-026-11677-5

Keywords: partial differential equations, machine learning, physics-informed neural networks, neural operators, finite element methods, hybrid computational methods, scientific machine learning, structure-preserving discretization, error quantification, multiphysics simulation, foundation models, carbon dioxide storage

Neural operators have quietly become one of the most consequential tools in computational science. Instead of learning a mapping between finite vectors, they learn mappings between functions, which makes them natural solvers for partial differential equations. Given a family of PDEs describing, say, fluid flow through porous rock or heat diffusing through a material, a trained neural operator can predict the full solution field for a new set of parameters almost instantly, bypassing the expensive numerical solvers that would otherwise be required. Classical architectures such as DeepONet and the Fourier neural operator have transformed this landscape, but their quantum counterparts have lagged behind, hampered by processing overheads and theoretical gaps about what quantum circuits can actually represent.

The central obstacle has been scaling. Many quantum machine-learning paradigms demand qubit counts or circuit depths that grow so quickly with problem size that they collapse into impracticality on near-term hardware. The Shanghai team, led by Ruocheng Wang, Xiaoqiu Zhong, Zhuo Xia and Junchi Yan, attacked the problem from two directions at once: they built a leaner architecture and, crucially, they proved something rigorous about its power.

The theoretical centerpiece is an extension of the universal approximation theorem to the quantum domain for continuous nonlinear operators. Universal approximation, first established for classical neural networks in the 1990s, guarantees that sufficiently wide networks can represent a broad class of functions; the operator version underpins DeepONet. Proving an analogous guarantee for quantum circuits closes a foundational gap, but the team went further. Departing from the conventional view that quantum advantage must flow from the exponential size of Hilbert space, they showed that the architecture’s density matrix implicitly constructs a quadratic feature frame.

That quadratic frame yields a striking expressivity bound. For operators, the implicit feature space scales as O(p²) in the number of parameters p, circumventing the O(p) linear capacity limits of matched classical models. In plain terms, each additional parameter in the quantum model buys roughly a square’s worth of representational capacity compared with a classical model of the same size. This is a subtle but meaningful advantage: it does not rely on exotic claims about exponentially large state spaces, but on a concrete, provable property of how the quantum circuit encodes features.

The second innovation addresses a practical bottleneck known as spectrum alignment. Quantum models encode input data through frequency modulation, and capturing high-frequency components of a solution, the sharp gradients and fine oscillations that matter in real PDEs, typically requires either deep circuits or many parameters. The researchers introduced a trainable-frequency strategy, dubbed TF-QuanONet, in which the base frequencies of the encoding adaptively space themselves during training. The network effectively learns which frequencies to emphasize, capturing relatively high-frequency structure without inflating the parameter count or the circuit depth.

The benchmarks are where the claims meet reality. Across extensive experiments, TF-QuanONet notably outperformed competing quantum baselines and achieved accuracy competitive with classical frameworks under strictly matched-parameter conditions, a fairness constraint that quantum machine-learning comparisons often fail to honor. More intriguing still is what happened as the problems grew. In high-dimensional scaling regimes, with latent dimensions p approaching 256, the quantum architecture exhibited superior optimization robustness, consistently converging to its intrinsic error floor while classical baselines suffered from high variance. The quantum model was not just accurate; it was reliably trainable where its classical competitors became erratic.

The team also tested the architecture on real IBM quantum processors, including the ibm_fez device, as a qualitative proof of concept. Comparisons between noise-free simulations and physical hardware demonstrated that QuanONet retains functional resilience on near-term machines, a nontrivial achievement given that real qubits decohere, gates misfire, and measurement noise corrupts outputs. The experiments spanned a range of canonical problems, including dynamical systems, advection equations and Darcy flow, with visualizations confirming that predictions track ground-truth solutions across varying input frequencies.

The work arrives amid a broader reckoning in quantum machine learning, where researchers have grown wary of claims that evaporate under fair comparison or realistic hardware assumptions. By grounding its architecture in a proven expressivity theorem, keeping resource requirements modest, and validating on commercial hardware, the study offers a template for what credible quantum advantage in scientific machine learning might look like. The code has been released publicly on GitHub and archived on Zenodo, and all datasets were generated directly from it, inviting the community to scrutinize and extend the results.

Whether the quadratic expressivity edge translates into decisive practical wins as quantum hardware improves remains an open question, but the study reframes the debate. Rather than waiting for fault-tolerant machines or betting everything on exponential Hilbert spaces, it demonstrates that carefully designed quantum architectures, with theory and engineering aligned, can already hold their own against strong classical baselines on the noisy processors available today.

Subject of Research: A quantum neural operator architecture with a proven quadratic expressivity bound for solving partial differential equations on near-term quantum hardware.

Article Title: Quantum neural operators with implicit quadratic frame and expressivity advantages

Article References: Wang, R., Zhong, X., Xia, Z., & Yan, J. (2026). Quantum neural operators with implicit quadratic frame and expressivity advantages. Nature Machine Intelligence. https://doi.org/10.1038/s42256-026-01289-7

Image Credits: AI Generated

DOI: 10.1038/s42256-026-01289-7

Keywords: quantum machine learning, neural operators, partial differential equations, QuanONet, NISQ era, universal approximation, expressivity, trainable frequencies, IBM quantum processors, DeepONet, quantum computing, scientific machine learning

The survey’s central argument is that weather and climate represent an unusually demanding, and unusually revealing, testbed for artificial intelligence. Unlike image recognition or language modelling, atmospheric science confronts machine-learning systems with petabyte-scale spatiotemporal data spread across a rotating sphere, governed by partial differential equations and constrained by global observational and reanalysis archives. On top of that sits a challenge that most mainstream AI benchmarks simply do not have: climate non-stationarity. The statistical properties of the atmosphere are themselves shifting as the planet warms, which means models trained on the past may be silently invalidated by the very future they are asked to predict. The authors argue that this combination of scale, physics and drift makes meteorology a proving ground whose lessons generalize far beyond forecasting.

To organize an enormous and sometimes chaotic literature, the survey classifies the major AI architectures by their physical inductive biases — the built-in assumptions each design makes about the structure of the world. Convolutional neural networks, the workhorses of early deep-learning weather prediction, assume local spatial structure and translation invariance. Graph neural networks treat the atmosphere as an irregular mesh, naturally handling the geometry of the sphere and unstructured computational grids. Transformers bring global attention mechanisms that can capture long-range teleconnections such as the El Niño–Southern Oscillation and the Madden–Julian oscillation, which link weather patterns across entire hemispheres. Generative models, including generative adversarial networks and diffusion-based approaches, address a different problem entirely: producing realistic ensembles and downscaling coarse global fields to fine local detail.

Two unifying mathematical themes run through this taxonomy. The first is geometric deep learning, the program of designing networks whose internal operations respect the symmetries of the underlying space — in this case, rotation and translation on a sphere rather than on a flat plane. The second is operator learning, exemplified by neural operators such as the Fourier neural operator and its spherical variant, which learn mappings between entire function spaces rather than between individual data points. This distinction matters because weather and climate models are fundamentally functions of functions: they map one continuous field of temperature, pressure and wind onto another. Architectures that respect the spherical geometry of the planet and learn operators rather than fixed-resolution maps are, the authors argue, better positioned to generalize across resolutions and physical regimes.

Beyond architecture, the survey gives systematic treatment to three areas it considers underappreciated. Representation learning and foundation models — large networks pre-trained on vast atmospheric archives and then adapted to many downstream tasks — are examined as the emerging backbone of the field. Uncertainty quantification receives extensive attention, covering techniques from Bayesian approaches to ensemble generation, all aimed at answering the question operational forecasters care most about: not just what will happen, but how confident we should be. And causal discovery is framed as a complement to pure prediction, a way of using machine learning not merely to reproduce correlations in reanalysis data but to probe the physical mechanisms connecting them — a distinction that becomes critical when the climate itself is changing.

The paper’s most provocative contribution, however, is its naming and dissection of what the authors call evaluation pathologies in scientific machine learning. The first is the RMSE smoothness bias. Because root mean square error and mean-squared-error training objectives penalize sharp, spatially displaced features more harshly than blurry, averaged ones, models optimized on these metrics are systematically pushed toward smooth, blurred forecasts. A prediction that gets the shape of a storm exactly right but places it a few dozen kilometers off can score worse than a smeared, featureless field that is wrong everywhere but mildly. The practical consequence is that the metrics used to declare AI models superior to numerical weather prediction may be quietly selecting for aesthetically smooth mediocrity while penalizing the crisp, high-impact detail that matters most to forecasters and the public.

The second pathology the authors identify is ERA5 training–evaluation circularity. ERA5, the European Centre for Medium-Range Weather Forecasts’ flagship reanalysis, is the de facto training ground for most AI weather models — but it is also the reference against which those models are scored. A model trained to reproduce ERA5 and then evaluated against ERA5 is, in a meaningful sense, being graded on its own homework. The circularity inflates apparent skill, obscures the reanalysis’s own biases, and makes it difficult to know how models would perform against genuinely independent observations. The third pathology, benchmark overfitting, compounds the problem: as the community iterates on a small set of standard test cases, models increasingly specialize to those cases, and leaderboard gains stop translating into real-world forecasting skill.

The survey does not stop at diagnosis. It frames the field’s open problems as scientific machine learning challenges that extend well beyond meteorology. Distribution shift under a non-stationary climate is the paradigm case: any AI system deployed over years must cope with input statistics that drift, potentially violating the stationarity assumptions baked into training. Physical consistency of learned operators — whether a neural network’s predictions obey conservation laws and dynamical constraints even far from its training distribution — remains unsolved. Sample efficiency in data-sparse regimes, such as the ocean interior, polar regions and the developing world’s observation networks, tests whether foundation-model approaches can transfer knowledge to places with few measurements. And the authors argue for intrinsic interpretability: not post-hoc explanations bolted onto a black box, but models whose internal reasoning is transparent enough for scientists to trust and interrogate, a theme connected to the explainable AI research program the work was partly funded to advance.

Why does this matter now? Because the operational stakes are rising fast. Deep-learning weather prediction systems are already being trialed by major forecasting centers, and skill on benchmarks is being cited as evidence they can replace or supplement physics-based simulation. If the benchmarks reward blur and circularity, the field risks institutionalizing models that look excellent on paper while underperforming on the rare, extreme events — hurricanes, heat waves, flash floods — where forecasts save lives. The survey’s argument is that verification against rare extremes, using metrics such as the fractions skill score and the continuous ranked probability score alongside traditional correlation measures, must become central rather than peripheral to how AI forecasters are judged.

The broader lesson, the authors contend, is that weather and climate offer scientific machine learning a uniquely honest mirror. The domain combines massive data, hard physics, distribution drift and unforgiving operational verification — a combination that strips away the comfortable assumptions of mainstream AI benchmarking. The survey, published open access with funding support from the Austrian Science Fund and the European Union’s Horizon Europe RI-SCALE project, is intended as both a map and a challenge: a structured account of where AI methods for the atmosphere stand today, and a warning that the path forward runs through better evaluation, not just bigger models. If the field heeds it, the same rigor that makes forecasting trustworthy in a changing climate could reshape how machine learning is validated across the sciences.

Subject of Research: Artificial intelligence methods, benchmarking, and scientific machine learning challenges for weather and climate prediction

Article Title: Artificial intelligence for weather and climate: a survey of methods, benchmarks, and scientific machine learning challenges

Article References: Holzinger, A., Fiore, S., Degiacomi, T., Antonio, F., & Müller, H. (2026). Artificial intelligence for weather and climate: a survey of methods, benchmarks, and scientific machine learning challenges. Artificial Intelligence Review. https://doi.org/10.1007/s10462-026-11690-8

Image Credits: AI Generated

DOI: 10.1007/s10462-026-11690-8

Keywords: artificial intelligence, weather forecasting, climate modeling, machine learning, neural operators, geometric deep learning, uncertainty quantification, benchmark design, distribution shift, spatiotemporal learning, foundation models, scientific machine learning

The core problem the work addresses is a familiar one to anyone who has tried to redesign an enzyme. Physics-based approaches can predict how a mutation will shift catalytic rates, binding affinities or thermal stability, but they demand deep expertise and laborious simulation. Language models, by contrast, can propose sequences in seconds, yet their suggestions often arrive as opaque outputs divorced from the mechanistic reasoning that experimentalists rely on. MutexaGPT is framed as an intuition-to-design translator: it takes mechanistic hypotheses expressed in natural language and converts them into concrete, physically grounded sequence modifications, while explaining its proposals in terms an enzyme engineer can interrogate.

Underneath, the system combines a large language model interface with physics-based scoring of candidate mutations. Rather than allowing the language model to generate sequences freely, the framework constrains its output so that every proposed change must be consistent with quantitative estimates of energetic effects on the protein structure. This mutual constraint, reflected in the ‘mu’ at the heart of the tool’s name, is what distinguishes it from purely generative pipelines. The language model supplies fluency, breadth of protein knowledge and an accessible conversational front end; the physical models supply a hard filter that discards proposals which look plausible in sequence space but would destabilize the fold or disrupt the catalytic machinery.

The promise of such a translator becomes clear when considering how enzyme engineers actually work. A typical project might begin with a hypothesis: that a specific loop near the active site is too rigid, limiting substrate access, or that a particular charged residue destabilizes a transition state. Traditionally, translating that hypothesis into a mutation library requires molecular dynamics simulations, free-energy calculations and statistical thermodynamic modeling, often weeks of specialist work. With an intuition-to-design interface, a researcher could describe the hypothesis in plain language and receive ranked candidate mutations, each annotated with the physical reasoning behind its predicted effect. The expertise moves from operating simulation software to judging scientific arguments.

This shift has implications well beyond convenience. Protein engineering sits at the center of some of the most urgent challenges in biotechnology, from designing enzymes that break down plastics to developing therapeutics and industrial catalysts that operate under harsh conditions. If the bottleneck in these projects is partly a communication bottleneck, between the scientists who understand the biology and the models that explore sequence space, then a translator that removes that friction could accelerate design cycles across the field. The framework suggests a future in which the loop of hypothesis, design, prediction and experimental test tightens from months to days.

The approach also speaks to a growing concern about trust in AI-assisted science. Generative protein models have produced striking successes, including novel folds and binders validated in the laboratory, but critics note that their recommendations can be scientifically hollow: a sequence that works without an explanation teaches the field little. By requiring every proposal to pass through a physics-based checkpoint and by returning mechanistic justifications, MutexaGPT-style systems aim to keep the human expert in the loop, not as a passive approver but as an active scientific interlocutor who can challenge, refine and learn from the model’s reasoning.

There are, of course, substantial technical hurdles. Physics-based energy functions remain approximations, and their accuracy varies with protein class, solvent conditions and the nature of the mutation. A translator is only as reliable as the physical models it consults, and systematic errors in those models could propagate into confident but flawed design recommendations. Equally, large language models can hallucinate mechanistic rationales that sound persuasive but do not correspond to the actual scoring calculation. Robust systems will need to keep the explanatory layer tightly coupled to the underlying physics, ensuring that what the model says about a mutation matches what the energy calculations imply.

The framework also raises questions about how such tools should be evaluated. A purely generative model can be scored by the success rate of its designs in the lab. A translator, however, must also be judged on the quality of its scientific communication: whether its explanations help experts form better hypotheses, catch their own errors and understand why a design failed. Designing benchmarks for that kind of scientific dialogue is an open problem, and one that the field of AI for science is only beginning to confront. Early enthusiasm for conversational research assistants has been tempered by recognition that fluency is not the same as insight.

What makes the appearance of this framework notable is its timing. Protein language models have matured rapidly, physics-based design tools have become more accessible, and experimental validation pipelines, particularly those based on high-throughput screening and automated laboratories, can now process large numbers of designs quickly. The missing element has been the connective tissue between these components. An intuition-to-design translator positions itself as exactly that connective tissue, embedding established physical modeling inside a conversational interface rather than replacing it with end-to-end black boxes.

For the broader community, the arrival of MutexaGPT signals a possible direction for AI in experimental science generally: not models that replace domain expertise, but models that metabolize it, turning accumulated mechanistic understanding into design actions and returning physical explanations that sharpen that understanding further. If that loop works as intended, the winners will be the enzyme engineers whose intuitions, long locked inside papers and protocols, suddenly become executable instructions for exploring a protein universe far larger than any laboratory could ever sample by hand.

Subject of Research: Physics-based enzyme engineering using a large language model translator framework called MutexaGPT

Article Title: MutexaGPT: an intuition-to-design translator for physics-based enzyme engineering

Article References: Shao, Q., Zhong, Y., Stull, S., Ran, X., Ding, N., Nehil-Puleo, K., Yao, R., Xu, H., & Yang, Z. J. (2026). MutexaGPT: an intuition-to-design translator for physics-based enzyme engineering. Nature Computational Science. https://doi.org/10.1038/s43588-026-01049-y

Image Credits: AI Generated

DOI: 10.1038/s43588-026-01049-y

Keywords: MutexaGPT, enzyme engineering, protein design, large language models, physics-based modeling, computational biology, biotechnology, protein stability, AI for science, mutagenesis, enzyme catalysis, scientific machine learning