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We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure…

Stochastic differential equations are commonly used to describe the evolution of stochastic processes. The state uncertainty of such processes is best represented by the probability density function (PDF), whose evolution is governed by the…

Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…

The accuracy of solving partial differential equations (PDEs) on coarse grids is greatly affected by the choice of discretization schemes. In this work, we propose to learn time integration schemes based on neural networks which satisfy…

Time series forecasting is a challenging task due to the existence of complex and dynamic temporal dependencies. This can lead to incorrect predictions by even the best forecasting models. Using more training data is one way to improve the…

Neural PDE solvers are increasingly used as learned surrogates for families of partial differential equations, where the key machine learning challenge is not only interpolation on a fixed benchmark distribution but generalization under…

Chaos is a fundamental feature of many complex dynamical systems, including weather systems and fluid turbulence. These systems are inherently difficult to predict due to their extreme sensitivity to initial conditions. Many chaotic systems…

Fourier Neural Operators (FNOs) have emerged as promising surrogates for partial differential equation solvers. In this work, we extensively tested FNOs on a variety of systems with non-linear and non-stationary properties, using a wide…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

In neural combinatorial optimization (CO), reinforcement learning (RL) can turn a deep neural net into a fast, powerful heuristic solver of NP-hard problems. This approach has a great potential in practical applications because it allows…

Scalability of graph neural networks remains one of the major challenges in graph machine learning. Since the representation of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes…

We present a method for fast and accurate physics-based predictions during non-prehensile manipulation planning and control. Given an initial state and a sequence of controls, the problem of predicting the resulting sequence of states is a…

Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require…

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…

Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional…

Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…

Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of…

Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…

Solving NP-hard/complete combinatorial problems with neural networks is a challenging research area that aims to surpass classical approximate algorithms. The long-term objective is to outperform hand-designed heuristics for…

Computational Fluid Dynamics (CFD) is an important approach for analyzing flow phenomena and predicting engineering-relevant quantities. The governing physics is formulated as partial differential equations(PDEs) and solved numerically on…