Search Results for author:
Found 33 papers, 17 papers with code
Physics-Informed Neural Networks for Nonhomogeneous Material Identification in Elasticity Imaging
We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials.
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker-Planck Equation and Physics-informed Neural Networks
The Fokker-Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants, hence requiring the development of a data-driven modeling approach.
Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models
Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots.
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks
The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry.
On the convergence of physics informed neural networks for linear second-order elliptic and parabolic type PDEs
By adapting the Schauder approach and the maximum principle, we show that the sequence of minimizers strongly converges to the PDE solution in $C^0$.
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior.
hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition
We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-refinement via domain decomposition and projection onto space of high-order polynomials.
Reinforcement Learning for Active Flow Control in Experiments
We demonstrate experimentally the feasibility of applying reinforcement learning (RL) in flow control problems by automatically discovering active control strategies without any prior knowledge of the flow physics.
Fluid Dynamics Robotics
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
We propose new symplectic networks (SympNets) for identifying Hamiltonian systems from data based on a composition of linear, activation and gradient modules.
Physics-informed neural networks for inverse problems in nano-optics and metamaterials
In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies.
Computational Physics Optics
DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
This universal approximation theorem is suggestive of the potential application of neural networks in learning nonlinear operators from data.
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks
Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.
PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs
Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speedup for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations.
Physics-informed semantic inpainting: Application to geostatistical modeling
A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics.
Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models
We propose a potential flow generator with $L_2$ optimal transport regularity, which can be easily integrated into a wide range of generative models including different versions of GANs and flow-based models.
Trainability of ReLU networks and Data-dependent Initialization
In order to quantify the trainability, we study the probability distribution of the number of active neurons at the initialization.
Quantifying the generalization error in deep learning in terms of data distribution and neural network smoothness
To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness.
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs).
Dying ReLU and Initialization: Theory and Numerical Examples
Numerical examples are provided to demonstrate the effectiveness of the new initialization procedure.
A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
It is comprised of three NNs, with the first NN trained using the low-fidelity data and coupled to two high-fidelity NNs, one with activation functions and another one without, in order to discover and exploit nonlinear and linear correlations, respectively, between the low-fidelity and the high-fidelity data.
Computational Physics
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered measurements.
Nonlocal flocking dynamics: Learning the fractional order of PDEs from particle simulations
Instead of specifying the fPDEs with an ad hoc fractional order for nonlocal flocking dynamics, we learn the effective nonlocal influence function in fPDEs directly from particle trajectories generated by the agent-based simulations.
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Here, we propose a new method with the objective of endowing the DNN with uncertainty quantification for both sources of uncertainty, i. e., the parametric uncertainty and the approximation uncertainty.
Deep Learning of Vortex Induced Vibrations
Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field.
Collapse of Deep and Narrow Neural Nets
However, here we show that even for such activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability.
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data
We present hidden fluid mechanics (HFM), a physics informed deep learning framework capable of encoding an important class of physical laws governing fluid motions, namely the Navier-Stokes equations.
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering.
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations.
Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations
We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations.
Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire.
Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equations
Numerical Gaussian processes, by construction, are designed to deal with cases where: (1) all we observe are noisy data on black-box initial conditions, and (2) we are interested in quantifying the uncertainty associated with such noisy data in our solutions to time-dependent partial differential equations.
Machine Learning of Linear Differential Equations using Gaussian Processes
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations.
Inferring solutions of differential equations using noisy multi-fidelity data
For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditions for well-posed problems.
