Related papers: Physical Systems Modeled Without Physical Laws

Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…

Physical reservoir computing is a computational framework that implements spatiotemporal information processing directly within physical systems. By exciting nonlinear dynamical systems and creating linear models from their state, we can…

Whilst the partial differential equations that govern the dynamics of our world have been studied in great depth for centuries, solving them for complex, high-dimensional conditions and domains still presents an incredibly large…

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

Simulation of the dynamics of physical systems is essential to the development of both science and engineering. Recently there is an increasing interest in learning to simulate the dynamics of physical systems using neural networks.…

Machine learning approaches to spatiotemporal physical systems have primarily focused on next-frame prediction, with the goal of learning an accurate emulator for the system's evolution in time. However, these emulators are computationally…

Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…

Physics-based simulation of mesh based domains remains a challenging task. State-of-the-art techniques can produce realistic results but require expert knowledge. A major bottleneck in many approaches is the step of integrating a potential…

Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…

Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…

This paper discusses an approach for incorporating prior physical knowledge into the neural network to improve data efficiency and the generalization of predictive models. If the dynamics of a system approximately follows a given…

Combining physics with machine learning models has advanced the performance of machine learning models in many different applications. In this paper, we evaluate adding a weak physics constraint, i.e., a physics-based empirical…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

We propose a method for the data-driven inference of temporal evolutions of physical functions with deep learning. More specifically, we target fluid flows, i.e. Navier-Stokes problems, and we propose a novel LSTM-based approach to predict…

We consider the application of deep generative models in propagating uncertainty through complex physical systems. Specifically, we put forth an implicit variational inference formulation that constrains the generative model output to…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this two part…

To achieve virtual certification for industrial design, quantifying the uncertainties in simulation-driven processes is crucial. We discuss a physics-constrained approach to account for epistemic uncertainty of turbulence models. In order…

This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…