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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
This two part treatise introduces 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 and demonstrates how these networks can be used to infer solutions topartial differential equations, and obtain physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters.
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…
Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
- P. Perdikaris, M. Raissi, A. Damianou, N. Lawrence, G. Karniadakis
- Computer ScienceProceedings of the Royal Society A: Mathematical…
- 1 February 2017
A probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends is put forth.
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
Understanding and mitigating gradient pathologies in physics-informed neural networks
This work reviews recent advances in scientific machine learning with a specific focus on the effectiveness of physics-informed neural networks in predicting outcomes of physical systems and discovering hidden physics from noisy data and proposes a novel neural network architecture that is more resilient to gradient pathologies.
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems
This work puts forth a machine learning approach for identifying nonlinear dynamical systems from data that combines classical tools from numerical analysis with powerful nonlinear function approximators to distill the mechanisms that govern the evolution of a given data-set.
Machine learning of linear differential equations using Gaussian processes
When and why PINNs fail to train: A neural tangent kernel perspective
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
This work proposes a novel model class coined as physics-informed DeepONets, which introduces an effective regularization mechanism for biasing the outputs of DeepOnet models towards ensuring physical consistency, and demonstrates the effectiveness of the proposed framework through a series of comprehensive numerical studies across various types of PDEs.