Computing non-equilibrium trajectories by a deep learning approach

DOI10.1016/j.jcp.2023.112349arXiv2210.04042MaRDI QIDQ6095083

Eric Simonnet

Publication date: 27 November 2023

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2210.04042

zbMATH Keywords

neural networksinstantonsgeometric actionquasi-potentialFreidlin-Wentzell large deviation theorygMAM

Mathematics Subject Classification ID

Stochastic analysis (60Hxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Probabilistic methods, stochastic differential equations (65Cxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Computing transition rates for the 1-D stochastic Ginzburg-Landau-Allen-Cahn equation for finite-amplitude noise with a rare event algorithm
• Unbiasedness of some generalized adaptive multilevel splitting algorithms
• Simulation and estimation of extreme quantiles and extreme probabilities
• Statistical behaviour of adaptive multilevel splitting algorithms in simple models
• Study of noise-induced transitions in the Lorenz system using the minimum action method
• Symmetry-increasing bifurcation of chaotic attractors
• Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions
• Finding the quasipotential for nongradient SDEs
• DGM: a deep learning algorithm for solving partial differential equations
• A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
• Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Solving for high-dimensional committor functions using artificial neural networks
• Towards a theory of transition paths
• Combinatorial analysis of the adaptive last particle method
• Julia: A Fresh Approach to Numerical Computing
• Viscous Instanton for Burgers' Turbulence
• A trace formula for activated escape in noisy maps
• Adaptive Multilevel Splitting for Rare Event Analysis
• The instanton method and its numerical implementation in fluid mechanics
• The geometric minimum action method: A least action principle on the space of curves
• Probability density functions in steady-state Burgers turbulence
• Large fluctuations for a nonlinear heat equation with noise
• Deterministic Nonperiodic Flow
• Computation of minimum action paths of the stochastic nonlinear Schrödinger equation with dissipation
• Minimum action method for the study of rare events
• Instanton filtering for the stochastic Burgers equation
• Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
• Deep Splitting Method for Parabolic PDEs
• Computation of extreme heat waves in climate models using a large deviation algorithm
• Collapse of transitional wall turbulence captured using a rare events algorithm
• Coupling rare event algorithms with data-based learned committor functions using the analogue Markov chain
• Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
• Crises, sudden changes in chaotic attractors, and transient chaos
• Chaos, Scattering and Statistical Mechanics
• Fluctuations and Irreversible Process. II. Systems with Kinetic Energy
• Gel’fand–Yaglom type equations for calculating fluctuations around instantons in stochastic systems

This page was built for publication: Computing non-equilibrium trajectories by a deep learning approach