Diffuse optical tomography, or DOT, works by shining pulses of near-infrared light, roughly in the 700 to 1000 nanometer range, into biological tissue. Most photons are scattered by tissue structures and absorbed by hemoglobin and water, but a small fraction emerges back at the surface. Because anomalies such as bleeding sites and malignant tumors absorb more near-infrared photons than healthy tissue, the pattern of light that re-emerges carries information about the location, size, and nature of the hidden anomaly. Unlike X-ray-based methods, the technique involves no ionizing radiation, making it attractive for repeated monitoring of vulnerable patients, including newborns and stroke victims.

The most information-rich variant of the technique, time-domain DOT, measures not just how much light returns but when. A pulse lasting picoseconds is injected, and detectors record the temporal profile of the photons that make it back to the surface. Because photons that travel deeper into the tissue take longer to return, the shape of these time-resolved signals encodes the three-dimensional distribution of absorption and scattering within the tissue. A recently developed experimental setup with picosecond temporal resolution has made high-resolution reconstruction feasible—but reconstructing an image from the measurements requires solving what physicists call the forward problem: predicting what the detectors should see for a given configuration of tissue properties.

That forward problem is computationally brutal. Photon propagation through multiple-scattering tissue is governed by the radiative transfer equation, an integro-differential equation with no general analytical solution. Direct numerical solutions demand enormous processing time and memory because the intensity depends on position, direction, and time simultaneously. Common shortcuts come with trade-offs: Monte Carlo methods introduce statistical noise, while the widely used diffusion approximation is only valid where scattering is so frequent that the radiation field is nearly isotropic. The team, led by Shu Horie of the Center for Computational Sciences at the University of Tsukuba, avoided both pitfalls by drawing on TRINITY, a radiative transfer code originally developed by co-author Hidenobu Yajima and colleagues for near-infrared tomography. TRINITY solves the time-dependent radiative transfer equation directly using a ray-tracing method that minimizes numerical diffusion, and its outputs have already shown good agreement with phantom experiments. Recent enhancements incorporating wavelet transformations have further reduced its computational cost—but even the optimized code takes hours to simulate a single configuration, far too slow for a patient waiting at the bedside.

The researchers’ solution was to train a neural network to act as an emulator of those expensive simulations. They modeled a 4-centimeter cube of tissue, discretized into 128 cubed cells, containing a single spherical absorber representing a hemorrhage or tumor near the brain surface. The absorber’s absorption coefficient was set ten times higher than the surrounding tissue, mimicking the contrast of a real anomaly, while the scattering coefficient matched typical brain values. Light pulses were injected at the center of one face, and eight detectors arranged along a line 0.3 centimeters apart recorded the emerging signals over a 3-nanosecond window.

To cover the range of possible anomalies, the team ran 640 simulations, each with a different combination of the absorber’s horizontal position, depth, and radius, sampled using Latin hypercube sampling—a statistical technique that fills a multidimensional parameter space with minimal bias. The depth distribution was deliberately weighted toward shallow absorbers, because preliminary analysis showed that the measured signals are far more sensitive to anomalies less than about 2 centimeters from the surface. From each simulation, the researchers extracted two quantities at every detector: the normalized intensity of the returning light and an “absorption measure” defined as the fractional difference in signal relative to a tissue with no absorber at all. The absorption measure, which varies more dramatically with absorber properties, is considered especially suitable for diagnostics.

The neural network itself is compact and elegant. Built in PyTorch, it uses deep multi-task learning: a single input layer receives the three absorber features, a shared hidden layer of 32 neurons using ReLU activations extracts common structure, and task-specific branches with Tanh activations produce two outputs—254 values describing the time evolution of normalized intensity and 476 values describing the absorption measure at each detector. The network was trained with the Adam optimizer over 500 epochs, with hyperparameters selected through five-fold cross-validation. Training on a single CPU core took about 16 minutes for noiseless data and 2.3 hours for the noise-augmented variant.

The critical discovery of the study came from an unexpected direction: the best network was not the one trained on the cleanest data. When the team trained a network directly on the 640 pristine simulation outputs, it captured broad trends but failed badly on certain test cases, with prediction errors at some detectors exceeding acceptable thresholds—a classic signature of overfitting. When they instead duplicated the training data tenfold and injected Gaussian noise with a standard deviation of 0.01 into the signals, the network’s performance transformed. Its errors on unseen absorber configurations dropped to at most the level of the injected noise, and the worst-case loss across the test set fell by a factor of roughly 2.5. The noise, in effect, acted as a regularizer, allowing the network to generalize from the same underlying simulations without any additional computational expense.

The speed gain is the headline number. A single inference—predicting all the time-resolved signals for an arbitrary absorber configuration—takes about 2 milliseconds on a single Intel CPU, compared with hours for a full radiative transfer simulation, a speedup exceeding one million-fold. The team also benchmarked their emulator against Gaussian processes, a standard alternative for surrogate modeling, and found the competition wasn’t close: the Gaussian process prediction error for the most difficult test case reached 0.61, roughly 2000 times larger than the neural network’s error, and each Gaussian process inference took nearly four seconds.

Perhaps most importantly for clinical translation, the researchers demonstrated that the emulator can run the inverse problem—inferring an anomaly’s properties from measured light signals. Coupling the neural network with Markov Chain Monte Carlo sampling using the emcee package, they recovered the position, depth, and radius of test absorbers with the true values falling within the 68 percent credible regions of the inferred probability distributions. Radius uncertainties were on the order of a few hundredths of a centimeter. In other words, even with prediction errors comparable to the injected noise, the framework can robustly extract diagnostic parameters from optical data.

The approach has clear limits. The current model handles only a single spherical absorber with a fixed absorption coefficient, and performance degrades for anomalies lying very close to the pulse injection point, where the signals are exquisitely sensitive to small parameter changes—the team suggests that targeted additional simulations in that region of parameter space would be the most efficient remedy. Extending the feature space to include absorber shape, absorption strength, multiple anomalies, and other tissue types remains future work. But the demonstration that a modest fully connected network, trained on well-chosen simulation data and intelligently noise-augmented, can replace hours of physics computation with milliseconds of inference points to a plausible path toward DOT-based diagnosis that happens in real time—precisely the regime where early detection of brain hemorrhage and tumors saves lives.

In research published in Scientific Reports, Dudley, Magdaleno, Harding and colleagues show how mechanistic simulations can be used to improve scientific inference. The approach links two rapidly advancing fields: physics-based or process-based modeling, which attempts to reproduce how a system actually works, and machine learning, which excels at finding complex relationships in data. Together, they offer a route toward artificial intelligence that can estimate hidden scientific quantities, test explanations and make predictions even when direct measurements are incomplete.

Most neural networks learn by examining large collections of examples. During training, the system adjusts millions of internal parameters until its predictions become increasingly accurate. This strategy has transformed image recognition, language processing and automated decision-making, but it has an important weakness in scientific applications: a network can identify statistical correlations without understanding whether those correlations reflect genuine causation. If the data change, or if the network encounters conditions that were not represented during training, its predictions can fail dramatically.

Mechanistic simulations address that weakness by generating data from an explicit description of a system. Such a simulation may encode equations for physical forces, biological interactions, chemical reactions, population changes or other processes. Instead of simply recording what happened, the model represents why it happened. Researchers can then vary the underlying parameters, produce thousands or millions of synthetic observations and label each example with the hidden conditions that generated it. A neural network trained on those examples learns to reverse the process: given observable data, it estimates the unseen mechanisms or parameters responsible for them.

This is an inverse problem, and inverse problems are among the most difficult tasks in science. Measurements are often noisy, incomplete or indirect. Several different combinations of parameters may produce similar observations, a problem known as non-identifiability. A neural network can provide rapid estimates, but speed alone does not guarantee that the answer is scientifically meaningful. By training with mechanistic simulations, the researchers aim to constrain the network with information about the structure of the system, reducing the chance that it will rely on accidental features in a particular dataset.

The method also changes the economics of scientific discovery. Generating real-world observations can require expensive experiments, long-term monitoring or access to rare events. Simulations, by contrast, can produce controlled datasets at a fraction of the cost and can explore conditions that would be difficult or unethical to reproduce experimentally. A model can be exposed to extreme values, unusual combinations of variables and carefully designed perturbations, allowing researchers to investigate how its conclusions behave beyond the narrow range of existing measurements.

The technical advantage is especially important when a neural network must estimate parameters quickly. Traditional inference often involves repeatedly running a computationally demanding simulator while searching for the parameter values that best match observed data. This process can require thousands of simulations for a single case. Once trained, a neural network can approximate that inverse mapping in a fraction of the time. The simulator supplies the scientific structure during training, while the neural network provides speed during analysis.

The study’s central message is not that simulations can replace experiments, but that they can make machine-learning systems more disciplined and useful. A simulation is itself a hypothesis about how nature operates, and an inaccurate model can teach an AI system the wrong lessons. The researchers therefore emphasize the importance of testing whether conclusions learned from simulated data remain reliable when the network encounters observations from the real world. Differences between simulated and real measurements—known collectively as the simulation-to-real gap—can arise from noise, missing processes, calibration errors or assumptions built into the model.

Addressing that gap requires more than increasing the size of a neural network. Researchers may need to incorporate realistic measurement noise, compare predictions across multiple mechanistic models, use experimental data to recalibrate simulations and quantify uncertainty in the network’s output. Uncertainty is essential because a scientific estimate is not simply a number; it must also indicate how strongly the evidence supports that number. A well-designed system should be able to distinguish between a confident inference based on informative observations and an apparently precise answer produced when the available data cannot uniquely determine the underlying cause.

The growing interest in this approach reflects a broader change in scientific computing. Artificial intelligence is moving from tools that classify existing information toward systems that can assist with hypothesis testing, parameter estimation and model comparison. Neural networks trained on mechanistic simulations could help researchers analyze complex datasets in areas where direct interpretation is difficult, including biological systems, environmental processes and physical phenomena. Their greatest value may come not from producing an instant answer, but from narrowing the range of plausible explanations and revealing which additional measurements would most effectively discriminate between them.

The work also highlights a principle that is increasingly shaping the future of scientific AI: predictive performance should be connected to scientific validity. A model that performs well on a benchmark can still be misleading if it exploits shortcuts or fails under changed conditions. Mechanistic training offers a way to build those conditions into the learning process from the beginning. By combining equations, simulated experiments and data-driven algorithms, researchers can create systems that are faster than traditional inference methods while remaining anchored to explicit assumptions about the world.

As these methods mature, the critical test will be whether they improve reproducibility and discovery across independent datasets, laboratories and scientific disciplines. The most trustworthy systems will likely be hybrid: mechanistic simulations will provide structure, neural networks will provide computational efficiency, and real experiments will determine whether the resulting inferences survive contact with nature. The study by Dudley, Magdaleno, Harding and colleagues adds momentum to that vision, suggesting that the path to more capable scientific AI may not lie in abandoning scientific models, but in teaching machines to learn through them.

Subject of Research: Training neural networks on mechanistic simulations to improve scientific inference

Article Title: Training neural networks on mechanistic simulations improves scientific inference

Article References: Dudley, C., Magdaleno, R., Harding, C. et al. Training neural networks on mechanistic simulations improves scientific inference. Sci Rep (2026). https://doi.org/10.1038/s41598-026-64106-6

Image Credits: AI Generated

DOI: 10.1038/s41598-026-64106-6

Keywords: neural networks, mechanistic simulations, scientific inference, machine learning, inverse problems, computational modeling, simulation-to-real gap, uncertainty quantification, artificial intelligence