Related papers: Generalizable Physics-Informed Learning for Stocha…
Considerable research has been devoted to deep learning-based predictive models for system prognostics and health management in the reliability and safety community. However, there is limited study on the utilization of deep learning for…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…
In this paper, we propose a probabilistic physics-guided framework, termed Physics-guided Deep Markov Model (PgDMM). The framework targets the inference of the characteristics and latent structure of nonlinear dynamical systems from…
In this paper, we propose a method for bounding the probability that a stochastic differential equation (SDE) system violates a safety specification over the infinite time horizon. SDEs are mathematical models of stochastic processes that…
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…
Linear partial differential equations (PDEs) are an important, widely applied class of mechanistic models, describing physical processes such as heat transfer, electromagnetism, and wave propagation. In practice, specialized numerical…
The safety and resilience of civil infrastructure systems are increasingly threatened by compounded risks from various hazard events and structural deterioration due to environmental stressors. This study presents a comprehensive…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Despite its empirical success, deep learning still lacks a comprehensive theoretical understanding of model fitting and generalization. This paper proposes the probability distribution (PD) learning framework to analyze the optimization and…
Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…
Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
Decision Focused Learning has emerged as a critical paradigm for integrating machine learning with downstream optimisation. Despite its promise, existing methodologies predominantly rely on probabilistic models and focus narrowly on task…
Physics-informed neural networks solve partial differential equations by training neural networks. Since this method approximates infinite-dimensional PDE solutions with finite collocation points, minimizing discretization errors by…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…