PINF: Continuous Normalizing Flows for Physics-Constrained Deep Learning
The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability density conservation and enable the learning of complex data distributions. In this paper, we introduce Physics-Informed Normalizing Flows (PINF), a novel extension of continuous normalizing flows, incorporating diffusion through the method of characteristics. Our method, which is mesh-free and causality-free, can efficiently solve high dimensional time-dependent and steady-state Fokker-Planck equations.
Code (0)
등록된 구현이 없습니다.
Tasks
Deep LearningMethods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Fully differentiable model discovery
Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which …
modelModel DiscoverySpinFlow: A Physics-Informed Spin Field Framework for Traffic Phase Inference and Transition Detection
Active traffic management (ATM) is frequently hindered by traditional macroscopic models and rigid empirical thresholds that fail to capture metastable phase precursors, resulting in delayed, reactive interventions. To a…
Neural Diffeomorphic Non-uniform B-spline Flows
Normalizing flows have been successfully modeling a complex probability distribution as an invertible transformation of a simple base distribution. However, there are often applications that require more than invertibili…
Learning normalizing flows from Entropy-Kantorovich potentials
We approach the problem of learning continuous normalizing flows from a dual perspective motivated by entropy-regularized optimal transport, in which continuous normalizing flows are cast as gradients of scalar potential…
Self-Supervised Learning of Generative Spin-Glasses with Normalizing Flows
Spin-glasses are universal models that can capture complex behavior of many-body systems at the interface of statistical physics and computer science including discrete optimization, inference in graphical models, and au…
Self-Supervised Learning