Related papers: Physics-Informed Supervised Residual Learning for …

In this paper, we present the Residual Integral Solver Network (RISN), a novel neural network architecture designed to solve a wide range of integral and integro-differential equations, including one-dimensional, multi-dimensional, ordinary…

This paper introduces wavelet-physics-informed residual neural networks (W-PIRNNs) to study complex fluid flow problems by reconstructing the flow field from highly sparse, supervised data. Our W-PIRNNs fundamentally integrate ResNet and…

This work presents a multi-resolution physics-informed recurrent neural network (MR PI-RNN), for simultaneous prediction of musculoskeletal (MSK) motion and parameter identification of the MSK systems. The MSK application was selected as…

Deep Convolutional Neural Networks (CNNs) i.e. Residual Networks (ResNets) have been used successfully for many computer vision tasks, but are difficult to scale to 3D volumetric medical data. Memory is increasingly often the bottleneck…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Magnetic particle imaging reconstructs tracer distributions using a system matrix obtained through time-consuming, noise-prone calibration measurements. Methods for addressing imperfections in measured system matrices increasingly rely on…

The thesis focuses on various techniques to find an alternate approximation method that could be universally used for a wide range of CFD problems but with low computational cost and low runtime. Various techniques have been explored within…

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is…

Consistency of the predictions with respect to the physical forward model is pivotal for reliably solving inverse problems. This consistency is mostly un-controlled in the current end-to-end deep learning methodologies proposed for the…

Recently, Convolutional Neural Networks (CNNs) have shown promising performance in super-resolution (SR). However, these methods operate primarily on Low Resolution (LR) inputs for memory efficiency but this limits, as we demonstrate, their…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…

Materials discovery is crucial for making scientific advances in many domains. Collections of data from experiments and first-principle computations have spurred interest in applying machine learning methods to create predictive models…

A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims…

(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…

Our recent intensive study has found that physics-informed neural networks (PINN) tend to be local approximators after training. This observation leads to this novel physics-informed radial basis network (PIRBN), which can maintain the…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…

A physics-constrained neural network is presented for predicting the optical response of metasurfaces. Our approach incorporates physical laws directly into the neural network architecture and loss function, addressing critical challenges…

Physics-informed machine learning (PIML) provides a promising solution for building energy modeling and can serve as a virtual environment to enable reinforcement learning (RL) agents to interact and learn. However, challenges remain in…