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Discovering the unknown governing equations of grid-connected inverters from external measurements holds significant attraction for analyzing modern inverter-intensive power systems. However, existing methods struggle to balance the…

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited,…

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…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Machine Learning (ML) has recently been demonstrated to rival expert-level human accuracy in prediction and detection tasks in a variety of domains, including medicine. Despite these impressive findings, however, a key barrier to the full…

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been…

Compared to physics-based computational manufacturing, data-driven models such as machine learning (ML) are alternative approaches to achieve smart manufacturing. However, the data-driven ML's "black box" nature has presented a challenge to…

Physics-informed extreme learning machine (PIELM) has recently received significant attention as a rapid version of physics-informed neural network (PINN) for solving partial differential equations (PDEs). The key characteristic is to fix…

We propose a framework for training neural networks that are coupled with partial differential equations (PDEs) in a parallel computing environment. Unlike most distributed computing frameworks for deep neural networks, our focus is to…

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately current approaches fall short when the underlying space has a non trivial topology, and are only…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

Solving high-dimensional partial differential equations (PDEs) is a critical challenge where modern data-driven solvers often lack reliability and rigorous error guarantees. We introduce Simulation-Calibrated Scientific Machine Learning…

This paper presents two novel, physics-informed extreme learning machine (PIELM)-based algorithms for solving steady and unsteady nonlinear partial differential equations (PDEs) related to fluid flow. Although single-hidden-layer PIELMs…

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…

Particle Accelerators are high power complex machines. To ensure uninterrupted operation of these machines, thousands of pieces of equipment need to be synchronized, which requires addressing many challenges including design, optimization…

In recent years, deep learning-based methods have been proposed for solving inverse scattering problems (ISPs), but most of them heavily rely on data and suffer from limited generalization capabilities. In this paper, a new solving scheme…

Hysteresis is a ubiquitous phenomenon in science and engineering; its modeling and identification are crucial for understanding and optimizing the behavior of various systems. We develop an ordinary differential equation-based recurrent…