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Recent years have seen a surge in interest in building deep learning-based fully data-driven models for weather prediction. Such deep learning models if trained on observations can mitigate certain biases in current state-of-the-art weather…

Climate simulations are essential in guiding our understanding of climate change and responding to its effects. However, it is computationally expensive to resolve complex climate processes at high spatial resolution. As one way to speed up…

Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…

Neural population activity exhibits complex, nonlinear dynamics, varying in time, over trials, and across experimental conditions. Here, we develop Conditionally Linear Dynamical System (CLDS) models as a general-purpose method to…

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…

We introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white…

Machine learning models often require large datasets and struggle to generalize beyond their training distribution. These limitations pose significant challenges in scientific and engineering contexts, where generating exhaustive datasets…

A key objective in spatial statistics is to simulate from the distribution of a spatial process at a selection of unobserved locations conditional on observations (i.e., a predictive distribution) to enable spatial prediction and…

Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…

Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…

This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…

Many stochastic differential equations in various applications like coupled neuronal oscillators are driven by time-periodic forces. In this paper, we extend several data-driven computational tools from autonomous Fokker-Planck equation to…

This work recasts time-dependent optimal control problems governed by partial differential equations in a Dynamic Mode Decomposition with control framework. Indeed, since the numerical solution of such problems requires a lot of…

Diffusion models offer stable training and state-of-the-art performance for deep generative modeling tasks. Here, we consider their use in the context of multivariate subsurface modeling and probabilistic inversion. We first demonstrate…

We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…

The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering…

Stochastic mathematical models are essential tools for understanding and predicting complex phenomena. The purpose of this work is to study the exit times of a stochastic dynamical system-specifically, the mean exit time and the…

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…