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Integrating machine learning and multiscale modeling—perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences
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DeepXDE: A Deep Learning Library for Solving Differential Equations
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Coupled Time‐Lapse Full‐Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation
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Physically informed artificial neural networks for atomistic modeling of materials
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Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics
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Machine learning of linear differential equations using Gaussian processes
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Gaussian measure in Hilbert space and applications in numerical analysis
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Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks
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Stochastic spectral methods for efficient Bayesian solution of inverse problems
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SciANN: A Keras/TensorFlow wrapper for scientific computations and physics-informed deep learning using artificial neural networks
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Learning unknown physics of non-Newtonian fluids
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Training a 3-node neural network is NP-complete
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Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains
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Multi-Scale Deep Neural Network (MscaleDNN) Methods for Oscillatory Stokes Flows in Complex Domains
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Multigrid with Rough Coefficients and Multiresolution Operator Decomposition from Hierarchical Information Games
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Invariant Scattering Convolution Networks
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Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks
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Environmental Sensor Networks: A revolution in the earth system science?
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Physics‐Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems
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Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks
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Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
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PFNN: A penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries
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A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
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Deep learning of free boundary and Stefan problems
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Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
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A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems
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Coarse-graining auto-encoders for molecular dynamics
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Benchmark Analysis of Representative Deep Neural Network Architectures
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Error estimates for DeepONets: a deep learning framework in infinite dimensions
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hp-VPINNs: Variational physics-informed neural networks with domain decomposition
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Extraction of mechanical properties of materials through deep learning from instrumented indentation
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A jamming transition from under- to over-parametrization affects generalization in deep learning
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A Proposal on Machine Learning via Dynamical Systems
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Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks
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Conditional deep surrogate models for stochastic, high-dimensional, and multi-fidelity systems
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Learning dynamical systems from data: A simple cross-validation perspective, part I: Parametric kernel flows
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A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
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“Forget time”: Essay written for the FQXi contest on the Nature of Time
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Deep learning for universal linear embeddings of nonlinear dynamics
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Linking Machine Learning with Multiscale Numerics: Data-Driven Discovery of Homogenized Equations
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Ab initio solution of the many-electron Schrödinger equation with deep neural networks
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Artificial neural networks for solving ordinary and partial differential equations
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An Emergent Space for Distributed Data With Hidden Internal Order Through Manifold Learning
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The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
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Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
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Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions
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On some neural network architectures that can represent viscosity solutions of certain high dimensional Hamilton–Jacobi partial differential equations
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Deep Residual Learning for Image Recognition
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June 2016
Deep learning and process understanding for data-driven Earth system science
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February 2019
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data
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January 2021
Relu Deep Neural Networks and Linear Finite Elements
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Reynolds averaged turbulence modelling using deep neural networks with embedded invariance
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NeuroDiffEq: A Python package for solving differential equations with neural networks
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Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review
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Identification of distributed parameter systems: A neural net based approach
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DGM: A deep learning algorithm for solving partial differential equations
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fPINNs: Fractional Physics-Informed Neural Networks
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January 2019
Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization
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Geometric Deep Learning: Going beyond Euclidean data
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Fast Parallel Algorithms for Short-Range Molecular Dynamics
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Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification
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DISCRETE- vs. CONTINUOUS-TIME NONLINEAR SIGNAL PROCESSING OF Cu ELECTRODISSOLUTION DATA
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A point-cloud deep learning framework for prediction of fluid flow fields on irregular geometries
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Adversarial uncertainty quantification in physics-informed neural networks
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DPM: A deep learning PDE augmentation method with application to large-eddy simulation
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Uncovering turbulent plasma dynamics via deep learning from partial observations
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DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators
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Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics
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Large scale and linear scaling DFT with the CONQUEST code
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April 2020
Scaling description of generalization with number of parameters in deep learning
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Universal Differential Equations for Scientific Machine Learning
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August 2020
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
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AutoML: A survey of the state-of-the-art
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A robotic Intelligent Towing Tank for learning complex fluid-structure dynamics
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Inverse problems: A Bayesian perspective
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Enforcing statistical constraints in generative adversarial networks for modeling chaotic dynamical systems
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A composite neural network that learns from multi-fidelity data: Application to function approximation and inverse PDE problems
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Predicting molecular properties with covariant compositional networks
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
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Bayesian differential programming for robust systems identification under uncertainty
Yang, Yibo; Aziz Bhouri, Mohamed; Perdikaris, Paris
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2243
https://doi.org/10.1098/rspa.2020.0290
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A Limited Memory Algorithm for Bound Constrained Optimization
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Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
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Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 476, Issue 2239
https://doi.org/10.1098/rspa.2020.0334
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Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks
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Pushing the Limit of Molecular Dynamics with Ab Initio Accuracy to 100 Million Atoms with Machine Learning
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On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
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On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
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Inferring solutions of differential equations using noisy multi-fidelity data
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ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains
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DifferentialEquations.jl – A Performant and Feature-Rich Ecosystem for Solving Differential Equations in Julia
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Transformer Dissection: An Unified Understanding for Transformer’s Attention via the Lens of Kernel
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Proceedings of the 2019 Conference on Empirical Methods in Natural Language Processing and the 9th International Joint Conference on Natural Language Processing (EMNLP-IJCNLP)
https://doi.org/10.18653/v1/D19-1443
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January 2019
SympNets: Intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
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Kernel Flows: From learning kernels from data into the abyss
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DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks
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SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient
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Solving high-dimensional partial differential equations using deep learning
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Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions
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Discovering Physical Concepts with Neural Networks
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Understanding deep convolutional networks
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A mean field view of the landscape of two-layer neural networks
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Double-slit photoelectron interference in strong-field ionization of the neon dimer
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The Harvard Clean Energy Project: Large-Scale Computational Screening and Design of Organic Photovoltaics on the World Community Grid
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Metric-based upscaling
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Learning constitutive relations using symmetric positive definite neural networks
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Distilling Free-Form Natural Laws from Experimental Data
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Bayesian Numerical Homogenization
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Exascale Deep Learning for Climate Analytics
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Numerical Gaussian Processes for Time-Dependent and Nonlinear Partial Differential Equations
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Physics-Informed Neural Network for Ultrasound Nondestructive Quantification of Surface Breaking Cracks
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Deep neural network approach to forward-inverse problems
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Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces
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Neural-net-induced Gaussian process regression for function approximation and PDE solution
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MgNet: A unified framework of multigrid and convolutional neural network
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