Related papers: Physics-Informed Machine Learning with Conditional…

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Numerical simulations for engineering applications solve partial differential equations (PDE) to model various physical processes. Traditional PDE solvers are very accurate but computationally costly. On the other hand, Machine Learning…

This paper provides estimation and inference methods for a conditional average treatment effects (CATE) characterized by a high-dimensional parameter in both homogeneous cross-sectional and unit-heterogeneous dynamic panel data settings. In…

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

Time-dependent partial differential equations (PDEs) for classic physical systems are established based on the conservation of mass, momentum, and energy, which are ubiquitous in scientific and engineering applications. These PDEs are…

Deep learning has shown strong potential in modeling complex spatiotemporal dynamics. However, most existing methods depend on densely and uniformly sampled data, which is often unavailable in practice due to sensor and cost limitations. In…

Simulating parameter-dependent stochastic differential equations (SDEs) presents significant computational challenges, as separate high-fidelity simulations are typically required for each parameter value of interest. Despite the success of…

We present a novel approach to modeling the ground state mass of atomic nuclei based directly on a probabilistic neural network constrained by relevant physics. Our Physically Interpretable Machine Learning (PIML) approach incorporates…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity…

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and…

Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here…

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…