English
Related papers

Related papers: Graph Neural Ordinary Differential Equations for C…

200 papers

The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture…

Machine Learning · Computer Science 2024-05-16 Yan Shen , Fan Yang , Mingchen Gao , Wen Dong

Understanding the structure and dynamics of liquids is pivotal for the study of larger spatiotemporal processes, especially in glass-forming materials at low temperatures. Density scaling, observed in many molecular systems through…

Soft Condensed Matter · Physics 2024-10-29 Jaehyeok Jin , David R. Reichman , Jeppe C. Dyre , Ulf R. Pedersen

This work addresses the challenge of using a deep learning model to prune graphs and the ability of this method to integrate explainability into spatio-temporal problems through a new approach. Instead of applying explainability to the…

Machine Learning · Computer Science 2025-10-14 Javier García-Sigüenza , Mirco Nanni , Faraón Llorens-Largo , José F. Vicent

Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…

Optimization and Control · Mathematics 2020-04-28 Dmitry Pozharskiy , Noah J. Wichrowski , Andrew B. Duncan , Grigorios A. Pavliotis , Ioannis G. Kevrekidis

Scientists often use observational time series data to study complex natural processes, but regression analyses often assume simplistic dynamics. Recent advances in deep learning have yielded startling improvements to the performance of…

Machine Learning · Computer Science 2023-04-21 Cory Shain , William Schuler

The numerical solution of partial differential equations (PDEs) is challenging because of the need to resolve spatiotemporal features over wide length and timescales. Often, it is computationally intractable to resolve the finest features…

Disordered Systems and Neural Networks · Physics 2019-08-22 Yohai Bar-Sinai , Stephan Hoyer , Jason Hickey , Michael P. Brenner

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

Computational Physics · Physics 2026-03-24 Mengyi Chen , Pengru Huang , Kostya S. Novoselov , Qianxiao Li

Recent advances in deep learning frameworks have established valuable tools for analyzing the long-timescale behavior of complex systems such as proteins. Especially the inclusion of physical constraints, e.g. time-reversibility, was a…

Quantitative Methods · Quantitative Biology 2021-12-22 Andreas Mardt , Frank Noé

Machine-learned coarse-grained (MLCG) molecular dynamics is a promising option for modeling biomolecules. However, MLCG models currently require large amounts of data from reference atomistic molecular dynamics or substantial computation…

Biological Physics · Physics 2024-07-02 Aleksander E. P. Durumeric , Yaoyi Chen , Frank Noé , Cecilia Clementi

We present an effective evolution equation for a coarse-grained distribution function of a long-range-interacting system preserving the symplectic structure of the non-collisional Boltzmann, or Vlasov, equation. We first derive a general…

Statistical Mechanics · Physics 2020-07-01 Guido Giachetti , Alessandro Santini , Lapo Casetti

Seismogenic plate boundaries are presumed to behave in a similar manner to a densely packed granular medium, where fault and blocks systems rapidly rearrange the distribution of forces within themselves, as particles do in slowly sheared…

Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first principles. Some of these processes can also be successfully…

The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…

Machine Learning · Computer Science 2025-11-11 Andrew F. Ilersich , Prasanth B. Nair

Lossy data transformations by definition lose information. Yet, in modern machine learning, methods like data pruning and lossy data augmentation can help improve generalization performance. We study this paradox using a solvable model of…

Statistical Mechanics · Physics 2025-09-19 Alex Nguyen , David J. Schwab , Vudtiwat Ngampruetikorn

We propose the coarse-grained spectral projection method (CGSP), a deep learning-assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show CGSP can extract spectral components of many-body…

Quantum Physics · Physics 2021-02-03 Pinchen Xie , Weinan E

We propose a systematic method for learning stable and physically interpretable dynamical models using sampled trajectory data from physical processes based on a generalized Onsager principle. The learned dynamics are autonomous ordinary…

Dynamical Systems · Mathematics 2021-11-25 Haijun Yu , Xinyuan Tian , Weinan E , Qianxiao Li

The 'Doughnut' of social and planetary boundaries has emerged as a popular framework for assessing environmental and social sustainability. Here, we provide a proof-of-concept analysis that shows how machine learning (ML) methods can be…

Machine Learning · Computer Science 2025-12-05 Stefano Vrizzi , Daniel W. O'Neill

We present a promising coarse-graining strategy for linking micro- and mesoscales of soft matter systems. The approach is based on effective pairwise interaction potentials obtained from detailed atomistic molecular dynamics (MD)…

Soft Condensed Matter · Physics 2007-05-23 A. P. Lyubartsev , M. Karttunen , I. Vattulainen , A. Laaksonen

Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…

Methodology · Statistics 2026-04-01 Alejandro Calle-Saldarriaga , Paul F. V. Wiemann , Matthias Katzfuss

This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…

Social and Information Networks · Computer Science 2020-05-08 Michael T. Schaub , Jean-Charles Delvenne , Renaud Lambiotte , Mauricio Barahona