Related papers: A simple equivariant machine learning method for d…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…

This survey examines the broad suite of methods and models for combining machine learning with physics knowledge for prediction and forecast, with a focus on partial differential equations. These methods have attracted significant interest…

These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…

Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been…

In this paper, we present a robotic model-based reinforcement learning method that combines ideas from model identification and model predictive control. We use a feature-based representation of the dynamics that allows the dynamics model…

Foundation models have transformed machine learning for language and vision, but achieving comparable impact in physical simulation remains a challenge. Data heterogeneity and unstable long-term dynamics inhibit learning from sufficiently…

We apply methods of dynamical systems to study the behaviour of the Randall-Sundrum models. We determine evolutionary paths for all possible initial conditions in a 2-dimensional phase space and we investigate the set of accelerated models.…

This article investigates the modeling and control of Lagrangian systems involving non-conservative forces using a hybrid method that does not require acceleration calculations. It focuses in particular on the derivation and identification…

Slow-fast dynamical systems, i.e., singularly or non-singularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating…

Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…

We present an empirical study in the geometric task of learning interatomic potentials, which shows equivariance matters even more at larger scales; we show a clear power-law scaling behaviour with respect to data, parameters and compute…

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the…

Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering…

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…

This work presents the dual benefit of integrating imitation learning techniques, based on the dynamical systems formalism, with the visual servoing paradigm. On the one hand, dynamical systems allow to program additional skills without…

Machine learning has been increasingly applied in climate modeling on system emulation acceleration, data-driven parameter inference, forecasting, and knowledge discovery, addressing challenges such as physical consistency, multi-scale…

Learning is a physical process. Here, we aim to study a simple dynamical system composed of springs and sticks capable of arbitrarily approximating any continuous function. The main idea of our work is to use the sticks to mimic a…