George Em Karniadakis

research

∙ 05/18/2023

A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data

We propose a framework and an algorithm to uncover the unknown parts of ...

0 Elham Kiyani, et al. ∙

research

∙ 05/04/2023

A Generative Modeling Framework for Inferring Families of Biomechanical Constitutive Laws in Data-Sparse Regimes

Quantifying biomechanical properties of the human vasculature could deep...

0 Minglang Yin, et al. ∙

research

∙ 04/15/2023

Learning in latent spaces improves the predictive accuracy of deep neural operators

Operator regression provides a powerful means of constructing discretiza...

9 Katiana Kontolati, et al. ∙

research

∙ 03/22/2023

Leveraging Multi-time Hamilton-Jacobi PDEs for Certain Scientific Machine Learning Problems

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep conne...

0 Paula Chen, et al. ∙

research

∙ 03/20/2023

Bi-orthogonal fPINN: A physics-informed neural network method for solving time-dependent stochastic fractional PDEs

Fractional partial differential equations (FPDEs) can effectively repres...

0 Lei Ma, et al. ∙

research

∙ 03/19/2023

LNO: Laplace Neural Operator for Solving Differential Equations

We introduce the Laplace neural operator (LNO), which leverages the Lapl...

0 Qianying Cao, et al. ∙

research

∙ 03/15/2023

ViTO: Vision Transformer-Operator

We combine vision transformers with operator learning to solve diverse i...

0 Oded Ovadia, et al. ∙

research

∙ 03/03/2023

Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks

Deep neural networks are an attractive alternative for simulating comple...

0 Katarzyna Michałowska, et al. ∙

research

∙ 02/28/2023

A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions

Physics-informed neural networks (PINNs) as a means of solving partial d...

0 Michael Penwarden, et al. ∙

research

∙ 02/23/2023

Learning stiff chemical kinetics using extended deep neural operators

We utilize neural operators to learn the solution propagator for the cha...

0 Somdatta Goswami, et al. ∙

research

∙ 02/07/2023

Learning bias corrections for climate models using deep neural operators

Numerical simulation for climate modeling resolving all important scales...

0 Aniruddha Bora, et al. ∙

research

∙ 02/02/2023

Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils

Deep neural operators, such as DeepONets, have changed the paradigm in h...

0 Khemraj Shukla, et al. ∙

research

∙ 01/26/2023

A Hybrid Deep Neural Operator/Finite Element Method for Ice-Sheet Modeling

One of the most challenging and consequential problems in climate modeli...

0 Qizhi He, et al. ∙

research

∙ 01/05/2023

L-HYDRA: Multi-Head Physics-Informed Neural Networks

We introduce multi-head neural networks (MH-NNs) to physics-informed mac...

0 zongren-zou, et al. ∙

research

∙ 12/13/2022

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dime...

0 Min Zhu, et al. ∙

research

∙ 11/17/2022

SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations

We propose a Spiking Neural Network (SNN)-based explicit numerical schem...

0 Qian Zhang, et al. ∙

research

∙ 11/16/2022

Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology

In this paper, we propose the augmented physics-informed neural network ...

0 Zheyuan Hu, et al. ∙

research

∙ 10/31/2022

On the Geometry Transferability of the Hybrid Iterative Numerical Solver for Differential Equations

The discovery of fast numerical solvers prompted a clear and rapid shift...

0 Adar Kahana, et al. ∙

research

∙ 09/06/2022

How important are activation functions in regression and classification? A survey, performance comparison, and future directions

Inspired by biological neurons, the activation functions play an essenti...

9 Ameya D. Jagtap, et al. ∙

research

∙ 08/28/2022

A Hybrid Iterative Numerical Transferable Solver (HINTS) for PDEs Based on Deep Operator Network and Relaxation Methods

Iterative solvers of linear systems are a key component for the numerica...

4 Enrui Zhang, et al. ∙

research

∙ 08/21/2022

G2Φnet: Relating Genotype and Biomechanical Phenotype of Tissues with Deep Learning

Many genetic mutations adversely affect the structure and function of lo...

11 Enrui Zhang, et al. ∙

research

∙ 07/08/2022

Physics-Informed Deep Neural Operator Networks

Standard neural networks can approximate general nonlinear operators, re...

28 Somdatta Goswami, et al. ∙

research

∙ 05/23/2022

Fractional SEIR Model and Data-Driven Predictions of COVID-19 Dynamics of Omicron Variant

We study the dynamic evolution of COVID-19 cased by the Omicron variant ...

0 Min Cai, et al. ∙

research

∙ 05/17/2022

Function Regression using Spiking DeepONet

One of the main broad applications of deep learning is function regressi...

8 Adar Kahana, et al. ∙

research

∙ 05/16/2022

Scalable algorithms for physics-informed neural and graph networks

Physics-informed machine learning (PIML) has emerged as a promising new ...

20 Khemraj Shukla, et al. ∙

research

∙ 05/08/2022

Neural operator learning of heterogeneous mechanobiological insults contributing to aortic aneurysms

Thoracic aortic aneurysm (TAA) is a localized dilatation of the aorta re...

14 Somdatta Goswami, et al. ∙

research

∙ 04/20/2022

Deep transfer learning for partial differential equations under conditional shift with DeepONet

Traditional machine learning algorithms are designed to learn in isolati...

5 Somdatta Goswami, et al. ∙

research

∙ 04/11/2022

Learning two-phase microstructure evolution using neural operators and autoencoder architectures

Phase-field modeling is an effective mesoscale method for capturing the ...

8 Vivek Oommen, et al. ∙

research

∙ 04/05/2022

Discovering and forecasting extreme events via active learning in neural operators

Extreme events in society and nature, such as pandemic spikes or rogue w...

0 Ethan Pickering, et al. ∙

research

∙ 03/09/2022

On the influence of over-parameterization in manifold based surrogates and deep neural operators

Constructing accurate and generalizable approximators for complex physic...

18 Katiana Kontolati, et al. ∙

research

∙ 02/25/2022

Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems

Multiscale modeling is an effective approach for investigating multiphys...

14 Minglang Yin, et al. ∙

research

∙ 02/23/2022

Physics-informed neural networks for inverse problems in supersonic flows

Accurate solutions to inverse supersonic compressible flow problems are ...

12 Ameya D. Jagtap, et al. ∙

research

∙ 02/07/2022

Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations

We consider strongly-nonlinear and weakly-dispersive surface water waves...

1 Ameya D. Jagtap, et al. ∙

research

∙ 02/03/2022

Systems Biology: Identifiability analysis and parameter identification via systems-biology informed neural networks

The dynamics of systems biological processes are usually modeled by a sy...

7 Mitchell Daneker, et al. ∙

research

∙ 01/14/2022

SympOCnet: Solving optimal control problems with applications to high-dimensional multi-agent path planning problems

Solving high-dimensional optimal control problems in real-time is an imp...

7 Tingwei Meng, et al. ∙

research

∙ 09/28/2021

DynG2G: An Efficient Stochastic Graph Embedding Method for Temporal Graphs

Dynamic graph embedding has gained great attention recently due to its c...

7 Mengjia Xu, et al. ∙

research

∙ 09/20/2021

When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?

Physics-informed neural networks (PINNs) have become a popular choice fo...

51 Zheyuan Hu, et al. ∙

research

∙ 08/31/2021

GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems

We propose the GENERIC formalism informed neural networks (GFINNs) that ...

6 Zhen Zhang, et al. ∙

research

∙ 08/25/2021

Simulating progressive intramural damage leading to aortic dissection using an operator-regression neural network

Aortic dissection progresses via delamination of the medial layer of the...

21 Minglang Yin, et al. ∙

research

∙ 07/12/2021

Meta-learning PINN loss functions

We propose a meta-learning technique for offline discovery of physics-in...

7 Apostolos F Psaros, et al. ∙

research

∙ 06/05/2021

AOSLO-net: A deep learning-based method for automatic segmentation of retinal microaneurysms from adaptive optics scanning laser ophthalmoscope images

Adaptive optics scanning laser ophthalmoscopy (AOSLO) provides real-time...

21 Qian Zhang, et al. ∙

research

∙ 05/20/2021

Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions

We propose a new type of neural networks, Kronecker neural networks (KNN...

38 Ameya D. Jagtap, et al. ∙

research

∙ 05/20/2021

Physics-informed neural networks (PINNs) for fluid mechanics: A review

Despite the significant progress over the last 50 years in simulating fl...

58 Shengze Cai, et al. ∙

research

∙ 04/20/2021

Parallel Physics-Informed Neural Networks via Domain Decomposition

We develop a distributed framework for the physics-informed neural netwo...

1 Khemraj Shukla, et al. ∙

research

∙ 04/06/2021

A Caputo fractional derivative-based algorithm for optimization

We propose a novel Caputo fractional derivative-based optimization algor...

11 Yeonjong Shin, et al. ∙

research

∙ 02/21/2021

Convergence rate of DeepONets for learning operators arising from advection-diffusion equations

We present convergence rates of operator learning in [Chen and Chen 1995...

0 Beichuan Deng, et al. ∙

research

∙ 02/18/2021

Error estimates for DeepOnets: A deep learning framework in infinite dimensions

DeepOnets have recently been proposed as a framework for learning nonlin...

0 Samuel Lanthaler, et al. ∙

research

∙ 01/17/2021

Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates

We propose a simple but effective modification of the discriminators, na...

5 Liu Yang, et al. ∙

research

∙ 01/07/2021

Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

We develop fractional buffer layers (FBLs) to absorb propagating waves w...

0 Min Cai, et al. ∙

research

∙ 12/05/2020

Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks

We propose the Poisson neural networks (PNNs) to learn Poisson systems a...

12 Pengzhan Jin, et al. ∙

George Em Karniadakis

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