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Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…

The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…

Graph-based spatio-temporal neural networks are effective to model the spatial dependency among discrete points sampled irregularly from unstructured grids, thanks to the great expressiveness of graph neural networks. However, these models…

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…

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…

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent…

Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented…

Detecting dynamic patterns of task-specific responses shared across heterogeneous datasets is an essential and challenging problem in many scientific applications in medical science and neuroscience. In our motivating example of rodent…

Deep learning methods achieve remarkable predictive performance in modeling complex, large-scale data. However, assessing the quality of derived models has become increasingly challenging, as more classical statistical assumptions may no…

Bridging the sim-to-real gap remains a fundamental challenge in robotics, as accurate dynamic parameter estimation is essential for reliable model-based control, realistic simulation, and safe deployment of manipulators. Traditional…

A data-driven, model-free approach to modeling the temporal evolution of physical systems mitigates the need for explicit knowledge of the governing equations. Even when physical priors such as partial differential equations are available,…

This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…

The discovery of structure from time series data is a key problem in fields of study working with complex systems. Most identifiability results and learning algorithms assume the underlying dynamics to be discrete in time. Comparatively…

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, though convenient and quick to obtain,…

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…

The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…

Time-varying stochastic optimization problems frequently arise in machine learning practice (e.g. gradual domain shift, object tracking, strategic classification). Although most problems are solved in discrete time, the underlying process…