ArticleNational science review2024
EPR-Net: constructing a non-equilibrium potential landscape via a variational force projection formulation.
Article in National science review, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 5 papers.
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Who cites it
5 citing papers in PubMed.
- Cell dynamics on energy landscape: Comparing attractor detection in Boolean network and diffusion-based models under in silico gene perturbations.Quantitative biology (Beijing, China) · 2026Article
- ZENN: A thermodynamics-inspired computational framework for heterogeneous data-driven modeling.Proceedings of the National Academy of Sciences of the United States of America · 2026Article
- Deciphering cell-fate trajectories using spatiotemporal single-cell transcriptomic data.NPJ systems biology and applications · 2025Review
- Beyond metaphor: quantitative reconstruction of Waddington landscape and exploration of cellular behavior.Briefings in bioinformatics · 2025Review
- Integrating Dynamical Systems Modeling with Spatiotemporal scRNA-Seq Data Analysis.Entropy (Basel, Switzerland) · 2025Review
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Authors and funding
3 authors.
Funding
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Abstract
We present EPR-Net, a novel and effective deep learning approach that tackles a crucial challenge in biophysics: constructing potential landscapes for high-dimensional non-equilibrium steady-state systems. EPR-Net leverages a nice mathematical fact that the desired negative potential gradient is simply the orthogonal projection of the driving force of the underlying dynamics in a weighted inner-product space. Remarkably, our loss function has an intimate connection with the steady entropy production rate (EPR), enabling simultaneous landscape construction and EPR estimation. We introduce an enhanced learning strategy for systems with small noise, and extend our framework to include dimensionality reduction and the state-dependent diffusion coefficient case in a unified fashion. Comparative evaluations on benchmark problems demonstrate the superior accuracy, effectiveness and robustness of EPR-Net compared to existing methods. We apply our approach to challenging biophysical problems, such as an eight-dimensional (8D) limit cycle and a 52D multi-stability problem, which provide accurate solutions and interesting insights on constructed landscapes. With its versatility and power, EPR-Net offers a promising solution for diverse landscape construction problems in biophysics.
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Registered trials
Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.