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Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…

We develop an approach for Bayesian learning of spatiotemporal dynamical mechanistic models. Such learning consists of statistical emulation of the mechanistic system that can efficiently interpolate the output of the system from arbitrary…

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…

We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In…

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,…

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…

The posterior over Bayesian neural network (BNN) parameters is extremely high-dimensional and non-convex. For computational reasons, researchers approximate this posterior using inexpensive mini-batch methods such as mean-field variational…

Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…

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…

Gaussian Process (GP) regression has seen widespread use in robotics due to its generality, simplicity of use, and the utility of Bayesian predictions. The predominant implementation of GP regression is a nonparameteric kernel-based…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

Deep learning (DL)-based methods have achieved state-of-the-art performance for many medical image segmentation tasks. Nevertheless, recent studies show that deep neural networks (DNNs) can be miscalibrated and overconfident, leading to…

Bayesian neural networks (BNNs) have recently gained popularity due to their ability to quantify model uncertainty. However, specifying a prior for BNNs that captures relevant domain knowledge is often extremely challenging. In this work,…

Deep kernel learning is a promising combination of deep neural networks and nonparametric function learning. However, as a data driven approach, the performance of deep kernel learning can still be restricted by scarce or insufficient data,…

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…

We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher differential…

Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…

We propose a randomized physics-informed neural network (PINN) or rPINN method for uncertainty quantification in inverse partial differential equation (PDE) problems with noisy data. This method is used to quantify uncertainty in the…

Prior-data fitted networks (PFNs) have emerged as promising foundation models for prediction from tabular datasets, achieving state-of-the-art performance on small to moderate data sizes without tuning. While PFNs are motivated by Bayesian…