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Model correction is essential for reliable PDE learning when the governing physics is misspecified due to simplified assumptions or limited observations. In the machine learning literature, existing correction methods typically operate in…
Unsupervised representation learning seeks to recover latent generative factors, yet standard methods relying on statistical independence often fail to capture causal dependencies. A central challenge is identifiability: as established in…
This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
Subgrid parameterizations of mesoscale eddies continue to be in demand for climate simulations. These subgrid parameterizations can be powerfully designed using physics and/or data-driven methods, with uncertainty quantification. For…
Deep generative models are increasingly used to gain insights in the geospatial data domain, e.g., for climate data. However, most existing approaches work with temporal snapshots or assume 1D time-series; few are able to capture…
Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their…
End-to-end autonomous driving provides a feasible way to automatically maximize overall driving system performance by directly mapping the raw pixels from a front-facing camera to control signals. Recent advanced methods construct a latent…
Transformer-based entropy models have gained prominence in recent years due to their superior ability to capture long-range dependencies in probability distribution estimation compared to convolution-based methods. However, previous…
Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…
Current machine learning (ML)-based algorithms for filtering electroencephalography (EEG) time series data face challenges related to cumbersome training times, regularization, and accurate reconstruction. To address these shortcomings, we…
We propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based…
Recent work in synthetic data generation in the time-series domain has focused on the use of Generative Adversarial Networks. We propose a novel architecture for synthetically generating time-series data with the use of Variational…
We present Mechanistic PDE Networks -- a model for discovery of governing partial differential equations from data. Mechanistic PDE Networks represent spatiotemporal data as space-time dependent linear partial differential equations in…
This paper presents a novel Energy-Equidistributed adaptive sampling framework for multi-dimensional conservative PDEs, introducing both location-based and velocity-based formulations of Energy-Equidistributed moving mesh PDEs (EMMPDEs).…
Variational Autoencoders (VAEs) provide a theoretically-backed and popular framework for deep generative models. However, learning a VAE from data poses still unanswered theoretical questions and considerable practical challenges. In this…
Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…
Quantifying the impacts of anthropogenic global warming requires accurate Earth system model (ESM) simulations. Statistical bias correction and downscaling can be applied to reduce errors and increase the resolution of ESMs. However,…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and…