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Many physical systems exhibit nonlocal spatiotemporal behaviors described by integro-differential equations (IDEs). Classical methods for solving IDEs require repeatedly evaluating convolution integrals, whose cost increases quickly with…

Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this…

Neural operator (NO) architectures learn nonlinear maps between infinite-dimensional function spaces and are widely used to accelerate simulation and enable data-driven model discovery. While universality results ensure expressivity, they…

Controlling nonlinear dynamics is a long-standing problem in engineering. Harnessing known physical information to accelerate or constrain stochastic learning pursues a new paradigm of scientific machine learning. By linearizing nonlinear…

Neural Networks (NNs) have been extensively used for a wide spectrum of real-world regression tasks, where the goal is to predict a numerical outcome such as revenue, effectiveness, or a quantitative result. In many such tasks, the point…

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the…

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…

A significant increase in renewable energy production is necessary to achieve the UN's net-zero emission targets for 2050. Using power-electronic controllers, such as Phase Locked Loops (PLLs), to keep grid-tied renewable resources in…

Physics-informed neural networks (PINN) have recently emerged as a promising application of deep learning in a wide range of engineering and scientific problems based on partial differential equation (PDE) models. However, evidence shows…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…

Many real-world problems require sequential decisions under uncertainty: when to inject or withdraw gas from storage, how to rebalance a pension portfolio each month, what temperature profile to run through a pharmaceutical reactor chain.…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…