Related papers: On uniqueness in structured model learning
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…
Learning and predicting the dynamics of physical systems requires a profound understanding of the underlying physical laws. Recent works on learning physical laws involve generalizing the equation discovery frameworks to the discovery of…
Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…
Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…
Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be…
In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…
We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…
Inverse problems for Partial Differential Equations (PDEs) are crucial in numerous applications such as geophysics, biomedical imaging, and material science, where unknown physical properties must be inferred from indirect measurements. In…
Physics-Informed Neural Networks (PINNs) provide a powerful and general framework for solving Partial Differential Equations (PDEs) by embedding physical laws into loss functions. However, training PINNs is notoriously difficult due to the…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access to the full system state. This limits their use in partially…
Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…
Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or accurate resolution of their solutions may be intractable. Instead,…
Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…
We present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs…
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…
Uncertainty estimation in machine learning has traditionally focused on the prediction stage, aiming to quantify confidence in model outputs while treating learned representations as deterministic and reliable by default. In this work, we…
Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network…