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We introduce an approach for solving PDEs over manifolds using physics informed neural networks whose architecture aligns with spectral methods. The networks are trained to take in as input samples of an initial condition, a time stamp and…

Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

In this work we propose a deep adaptive sampling (DAS) method for solving partial differential equations (PDEs), where deep neural networks are utilized to approximate the solutions of PDEs and deep generative models are employed to…

Accelerating the solution of nonlinear partial differential equations (PDEs) while maintaining accuracy at coarse spatiotemporal resolution remains a key challenge in scientific computing. Physics-informed machine learning (ML) methods such…

This paper proposes a mesh-free computational framework and machine learning theory for solving elliptic PDEs on unknown manifolds, identified with point clouds, based on diffusion maps (DM) and deep learning. The PDE solver is formulated…

In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cord\`{e}s condition for solving both linear and fully nonlinear partial differential equations (PDEs) in non-divergence form, together with…

In this paper, we present a deep surrogate model for learning the Green's function associated with the reaction-diffusion operator in rectangular domain. The U-Net architecture is utilized to effectively capture the mapping from source to…

Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven…

Learning from demonstration has been widely studied in machine learning but becomes challenging when the demonstrated trajectories are unstructured and follow different objectives. This short-paper proposes PODNet, Plannable Option…

The success of deep learning has been due, in no small part, to the availability of large annotated datasets. Thus, a major bottleneck in current learning pipelines is the time-consuming human annotation of data. In scenarios where such…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…

This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…

Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…

Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…

We consider the problem of training a machine learning model over a network of nodes in a fully decentralized framework. The nodes take a Bayesian-like approach via the introduction of a belief over the model parameter space. We propose a…

Finding accurate solutions to partial differential equations (PDEs) is a crucial task in all scientific and engineering disciplines. It has recently been shown that machine learning methods can improve the solution accuracy by correcting…

The partial differential equation (PDE) plays a significantly important role in many fields of science and engineering. The conventional case of the derivation of PDE mainly relies on first principles and empirical observation. However, the…