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Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Probabilistic graphical models (PGMs) serve as a powerful framework for modeling complex systems with uncertainty and extracting valuable insights from data. However, users face challenges when applying PGMs to their problems in terms of…

This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up…

Differentiable programming, enabled by automatic differentiation (AD), provides a robust framework for gradient-based optimization in computational plasma physics. While optimization is often only used towards design, we demonstrate that it…

Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…

We study reinforcement learning for controlled diffusion processes with unbounded continuous state spaces, bounded continuous actions, and polynomially growing rewards: settings that arise naturally in finance, economics, and operations…

Deep neural network learning can be formulated as a non-convex optimization problem. Existing optimization algorithms, e.g., Adam, can learn the models fast, but may get stuck in local optima easily. In this paper, we introduce a novel…

Physics-informed machine learning is gaining significant traction for enhancing statistical performance and sample efficiency through the integration of physical knowledge. However, current theoretical analyses often presume complete prior…

Diffusion Probabilistic Models (DPMs) have emerged as a powerful class of deep generative models, achieving remarkable performance in image synthesis tasks. However, these models face challenges in terms of widespread adoption due to their…

We introduce marginalization models (MAMs), a new family of generative models for high-dimensional discrete data. They offer scalable and flexible generative modeling by explicitly modeling all induced marginal distributions.…

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…

Distilling data into compact and interpretable analytic equations is one of the goals of science. Instead, contemporary supervised machine learning methods mostly produce unstructured and dense maps from input to output. Particularly in…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

Distributed machine learning has been widely studied in order to handle exploding amount of data. In this paper, we study an important yet less visited distributed learning problem where features are inherently distributed or vertically…

Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven models are pervasive, physical knowledge -- often expressed as…

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

Diffusion models have demonstrated remarkable performance in generating unimodal data across various tasks, including image, video, and text generation. On the contrary, the joint generation of multimodal data through diffusion models is…

In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine…

Learning general latent-variable probabilistic graphical models is a key theoretical challenge in machine learning and artificial intelligence. All previous methods, including the EM algorithm and the spectral algorithms, face severe…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…