# Blending Diverse Physical Priors with Neural Networks

@article{Ba2019BlendingDP, title={Blending Diverse Physical Priors with Neural Networks}, author={Yunhao Ba and Guangyuan Zhao and Achuta Kadambi}, journal={ArXiv}, year={2019}, volume={abs/1910.00201} }

Machine learning in context of physical systems merits a re-examination of the learning strategy. In addition to data, one can leverage a vast library of physical prior models (e.g. kinematics, fluid flow, etc) to perform more robust inference. The nascent sub-field of \emph{physics-based learning} (PBL) studies the blending of neural networks with physical priors. While previous PBL algorithms have been applied successfully to specific tasks, it is hard to generalize existing PBL methods to a…

## 18 Citations

### Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling

- Computer ScienceNeurIPS
- 2021

This work introduces an architecture of variational autoencoders (VAEs) in which a part of the latent space is grounded by physics, and proposes a regularized learning method that controls the effect of the trainable components and preserves the semantics of the physics-based latent variables as intended.

### PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics

- Computer ScienceKDD
- 2021

This work proposes a novel physics-informed GAN architecture, termed PID-GAN, where the knowledge of physics is used to inform the learning of both the generator and discriminator models, making ample use of unlabeled data instances.

### Kinematically consistent recurrent neural networks for learning inverse problems in wave propagation

- Computer ScienceArXiv
- 2021

This work attempts to perform physically interpretable learning of inverse problems in wave propagation without suffering overfitting restrictions using long short-term memory networks endowed with a physical, hyperparameter-driven regularizer, analogous to an artificial bulk modulus.

### Driven by Data or Derived Through Physics? A Review of Hybrid Physics Guided Machine Learning Techniques With Cyber-Physical System (CPS) Focus

- Computer ScienceIEEE Access
- 2020

A meticulous and systematic attempt at organizing and standardizing the methods of combining ML and MB models as hybrid learning methods and shedding some light on the challenges of hybrid models.

### Integrating Physics-Based Modeling with Machine Learning: A Survey

- Computer ScienceArXiv
- 2020

An overview of techniques to integrate machine learning with physics-based modeling and classes of methodologies used to construct physics-guided machine learning models and hybrid physics-machine learning frameworks from a machine learning standpoint is provided.

### A Framework for Machine Learning of Model Error in Dynamical Systems

- Computer ScienceCommunications of the American Mathematical Society
- 2022

A unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems from noisily and partially observed data is presented, and it is demonstrated numerically how data assimilation can be leveraged to learn hidden dynamics from noisy, partially-observed data.

### Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems

- Computer ScienceACM Computing Surveys
- 2022

A taxonomy of existing techniques that are able to integrate traditional physics-based modeling approaches with state-of-the-art machine learning (ML) techniques is provided, which uncovers knowledge gaps and potential crossovers of methods between disciplines.

### Physics vs. Learned Priors: Rethinking Camera and Algorithm Design for Task-Specific Imaging

- Computer Science2022 IEEE International Conference on Computational Photography (ICCP)
- 2022

This paper presents a framework to understand the building blocks of this nascent field of end-to-end design of camera hardware and algorithms, and shows how methods that exploit both physics and data have become prevalent in imaging and computer vision.

### Physics-Informed Discriminator (PID) for Conditional Generative Adversarial Nets

- Computer Science
- 2020

The proposed approach, termed as Physics-informed Discriminator for cGAN (cGANPID), is more aligned to the adversarial learning idea of cGAN as opposed to existing methods on incorporating physical knowledge in GANs by adding physics based loss functions as additional terms in the optimization objective of GAN.

### Process-guidance improves predictive performance of neural networks for carbon turnover in ecosystems

- Computer SciencebioRxiv
- 2022

Evaluation of the results under four classical prediction scenarios supports decision-making on the appropriate choice of a process-guided neural network for carbon fluxes in forest ecosystems.

## References

SHOWING 1-10 OF 53 REFERENCES

### Physics-based Neural Networks for Shape from Polarization

- PhysicsArXiv
- 2019

This work study the blending of physics and deep learning in the context of Shape from Polarization (SfP) in the framework of a two-stage encoder, finding that there is a subtlety to combining physics and neural networks.

### Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

- Computer ScienceArXiv
- 2017

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.

### End-to-End Differentiable Physics for Learning and Control

- Computer ScienceNeurIPS
- 2018

This paper demonstrates how to perform backpropagation analytically through a physical simulator defined via a linear complementarity problem, and highlights the system's ability to learn physical parameters from data, efficiently match and simulate observed visual behavior, and readily enable control via gradient-based planning methods.

### Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

- Computer ScienceJ. Mach. Learn. Res.
- 2018

This work puts forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time by approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks.

### Unrolled Optimization with Deep Priors

- Computer Science, MathematicsArXiv
- 2017

This paper presents unrolled optimization with deep priors, a principled framework for infusing knowledge of the image formation into deep networks that solve inverse problems in imaging, inspired by classical iterative methods.

### PDE-Net: Learning PDEs from Data

- Computer ScienceICML
- 2018

Numerical experiments show that the PDE-Net has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment.

### Physics-guided Neural Networks (PGNN): An Application in Lake Temperature Modeling

- Computer ScienceArXiv
- 2017

A novel framework, termed as physics-guided neural network (PGNN), leverages the output of physics-based model simulations along with observational features to generate predictions using a neural network architecture to ensure better generalizability as well as physical consistency of results.

### Label-Free Supervision of Neural Networks with Physics and Domain Knowledge

- Computer ScienceAAAI
- 2017

This work introduces a new approach to supervising neural networks by specifying constraints that should hold over the output space, rather than direct examples of input-output pairs, derived from prior domain knowledge.

### Neural Architecture Search with Reinforcement Learning

- Computer ScienceICLR
- 2017

This paper uses a recurrent network to generate the model descriptions of neural networks and trains this RNN with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation set.

### Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

- Computer ScienceArXiv
- 2017

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…