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Posterior distributions arising in ill-posed Bayesian inverse problems are often both analytically intractable and highly sensitive to parameters of the chosen prior family. We aim to understand the sensitivity of intractable posterior…

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…

We present a unified, finite-element-native variational inference framework for very high-dimensional Bayesian spatial field reconstruction in physics-based problems governed by partial differential equations (PDEs) that are nonlinear in…

Several studies explore inferences based on stochastic volatility (SV) models, taking into account the stylized facts of return data. The common problem is that the latent parameters of many volatility models are high-dimensional and…

Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…

In this article, we present a data-driven method for parametric models with noisy observation data. Gaussian process regression based reduced order modeling (GPR-based ROM) can realize fast online predictions without using equations in the…

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor…

This study proposes Structural Gating and Effect-aligned Discovery for Temporal Causal Discovery (SGED-TCD), a novel and general framework for lag-resolved causal discovery in complex multivariate time series. SGED-TCD combines explicit…

Stein Variational Gradient Descent (SVGD) is a highly efficient method to sample from an unnormalized probability distribution. However, the SVGD update relies on gradients of the log-density, which may not always be available. Existing…

We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing…

Volume conserving surface (VCS) models without deposition and evaporation, as well as ideal molecular-beam epitaxy models, are prototypes to study the symmetries of conserved dynamics. In this work we study two similar VCS models with…

This paper presents Robust samplE-based coVarIance StEering (REVISE), a multi-query algorithm that generates robust belief roadmaps for dynamic systems navigating through spatially dependent disturbances modeled as a Gaussian random field.…

This tutorial focuses on the fundamental architectures of Variational Autoencoders (VAE) and Generative Adversarial Networks (GAN), disregarding their numerous variations, to highlight their core principles. Both VAE and GAN utilize simple…

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's…

We develop the mathematical foundations of the stochastic modified equations (SME) framework for analyzing the dynamics of stochastic gradient algorithms, where the latter is approximated by a class of stochastic differential equations with…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

Deep generative models have shown tremendous capability in data density estimation and data generation from finite samples. While these models have shown impressive performance by learning correlations among features in the data, some…

Electrical Impedance Tomography (EIT) is a widely employed imaging technique in industrial inspection, geophysical prospecting, and medical imaging. However, the inherent nonlinearity and ill-posedness of EIT image reconstruction present…

While analytical solutions of critical (phase) transitions in physical systems are abundant for simple nonlinear systems, such analysis remains intractable for real-life dynamical systems. A key example of such a physical system is…

A Single Ensemble Empirical Mode Decomposition (SEEMD) is proposed for locating the damage in rolling element bearings. The SEEMD does not require a number of ensembles from the addition or subtraction of noise every time while processing…