Thursday, August 7, 2025
Science
No Result
View All Result
  • Login
  • HOME
  • SCIENCE NEWS
  • CONTACT US
  • HOME
  • SCIENCE NEWS
  • CONTACT US
No Result
View All Result
Scienmag
No Result
View All Result
Home Science News Mathematics

When Waddington meets Helmholtz: EPR-Net for constructing the potential landscapes of complex non-equilibrium systems

April 9, 2024
in Mathematics
Reading Time: 2 mins read
0
Constructing energy landscapes through enhanced EPR workflow.
65
SHARES
590
VIEWS
Share on FacebookShare on Twitter
ADVERTISEMENT
ADVERTISEMENT

The concept of Waddington landscape, originally proposed by British developmental biologist Conrad Hal Waddington in 1957, has been influential in describing the dynamical evolution of cellular development. Waddington’s metaphor of a ball rolling down a hill to represent cell differentiation has been widely adopted in epigenetics and developmental biology. However, quantitative characterization of these landscapes, particularly for high-dimensional systems, remains a challenging problem in computational biology.

Constructing energy landscapes through enhanced EPR workflow.

Credit: ©Science China Press

The concept of Waddington landscape, originally proposed by British developmental biologist Conrad Hal Waddington in 1957, has been influential in describing the dynamical evolution of cellular development. Waddington’s metaphor of a ball rolling down a hill to represent cell differentiation has been widely adopted in epigenetics and developmental biology. However, quantitative characterization of these landscapes, particularly for high-dimensional systems, remains a challenging problem in computational biology.

Led by Professor Tiejun Li (from Peking University) and Dr. Wei Zhang (from Freie Universität Berlin and Zuse Institute Berlin), together with Yue Zhao (first author, PhD student from Peking University), the study introduces EPR-Net, a deep learning method that effectively tackles this challenge.                

This method leverages the unique mathematical insight that the negative gradient of Waddington landscape corresponds to an extended Helmholtz decomposition in the context of non-equilibrium systems. This insight, closely related to the entropy production rate (EPR) in statistical physics, is a breakthrough that has not be recognized previously.

The research team demonstrates the power of EPR-Net through its application to various biological models, including those exhibiting multiple stable points, limit cycles, and strange attractors. Enhanced EPR-Net, an extension of the method, is also introduced. The study showcases the effectiveness of enhanced EPR on benchmark problems and its superiority over other methods. It also provides a unified framework to address landscape construction, dimensionality reduction, and problems with variable coefficients.

EPR-Net offers computational efficiency, eliminates the need for boundary conditions, and provides a clear physical interpretation that links directly to the entropy production rate in statistical physics.

To address the challenge of visualizing high-dimensional landscapes, the researchers also developed a dimensionality reduction strategy using EPR-Net. This strategy has been applied to study an 8-dimensional limit cycle system, where it gives accurate projections which not only closely match the system’s equilibrium distribution but also reveal new delicate structures not observed before.

“EPR-Net, with its elegant mathematical foundation and convex structure, promises to be an effective strategy for constructing energy landscape functions of high-dimensional NESS systems.” The researchers conclude. “We are currently exploring further extensions and applications of the method. We feel exciting because this powerful method has the potential to improve our understanding of many complex NESS systems by visualizing their potential landscapes.”

See the article:

EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation



Journal

National Science Review

DOI

10.1093/nsr/nwae052

Share26Tweet16
Previous Post

Avoidance, confusion, solitude: whales react to rising noise pollution

Next Post

Unlocking the secrets of black raspberry resilience: genome-wide discovery and analysis of bZIP transcription factors

Related Posts

blank
Mathematics

Researchers Discover a Natural ‘Speed Limit’ to Innovation

August 5, 2025
blank
Mathematics

World’s First Successful Parallelization of Cryptographic Protocol Analyzer Maude-NPA Drastically Cuts Analysis Time, Enhancing Internet Security

August 5, 2025
blank
Mathematics

Encouraging Breakthroughs in Quantum Computing

August 4, 2025
blank
Mathematics

Groundbreaking Real-Time Visualization of Two-Dimensional Melting Unveiled

August 4, 2025
blank
Mathematics

National Science Foundation Awards $16.5 Million to Renew Brown’s National Mathematics Institute

August 4, 2025
blank
Mathematics

Revolutionary Technique to Control Electricity in Atom-Thin Metals Promises to Transform Future Devices

August 4, 2025
Next Post
Figure 1.

Unlocking the secrets of black raspberry resilience: genome-wide discovery and analysis of bZIP transcription factors

  • Mothers who receive childcare support from maternal grandparents show more parental warmth, finds NTU Singapore study

    Mothers who receive childcare support from maternal grandparents show more parental warmth, finds NTU Singapore study

    27530 shares
    Share 11009 Tweet 6881
  • University of Seville Breaks 120-Year-Old Mystery, Revises a Key Einstein Concept

    942 shares
    Share 377 Tweet 236
  • Bee body mass, pathogens and local climate influence heat tolerance

    641 shares
    Share 256 Tweet 160
  • Researchers record first-ever images and data of a shark experiencing a boat strike

    506 shares
    Share 202 Tweet 127
  • Warm seawater speeding up melting of ‘Doomsday Glacier,’ scientists warn

    310 shares
    Share 124 Tweet 78
Science

Embark on a thrilling journey of discovery with Scienmag.com—your ultimate source for cutting-edge breakthroughs. Immerse yourself in a world where curiosity knows no limits and tomorrow’s possibilities become today’s reality!

RECENT NEWS

  • Shifting Rainfall Patterns in Euphrates-Tigris Basin
  • T. Gondii Infection Risks in Ethiopian Sheep, Goats
  • VAMP Proteins: Key Drivers of Disease and Therapy
  • Rising Melatonin Use in Children Sparks Global Concern

Categories

  • Agriculture
  • Anthropology
  • Archaeology
  • Athmospheric
  • Biology
  • Bussines
  • Cancer
  • Chemistry
  • Climate
  • Earth Science
  • Marine
  • Mathematics
  • Medicine
  • Pediatry
  • Policy
  • Psychology & Psychiatry
  • Science Education
  • Social Science
  • Space
  • Technology and Engineering

Subscribe to Blog via Email

Enter your email address to subscribe to this blog and receive notifications of new posts by email.

Join 5,184 other subscribers

© 2025 Scienmag - Science Magazine

Welcome Back!

Login to your account below

Forgotten Password?

Retrieve your password

Please enter your username or email address to reset your password.

Log In
No Result
View All Result
  • HOME
  • SCIENCE NEWS
  • CONTACT US

© 2025 Scienmag - Science Magazine

Discover more from Science

Subscribe now to keep reading and get access to the full archive.

Continue reading