Physics-informed Neural Networks for Encoding Dynamics in Real Physical Systems

• URL: http://arxiv.org/abs/2401.03534v1
• Date: Sun, 7 Jan 2024 16:19:28 GMT
• Title: Physics-informed Neural Networks for Encoding Dynamics in Real Physical Systems
• Authors: Hamza Alsharif
• Abstract summary: This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations. We show that for the pendulum system the PINNs outperformed equivalent uninformed neural networks (NNs) in the ideal data case. In similar test cases with real data collected from an experiment, PINNs outperformed NNs with 9.3x and 9.1x accuracy improvements for 67 linearly-spaced and uniformly-distributed random points respectively.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple nonlinear pendulum, and the second is 2D heat diffusion across the surface of a metal block. We show that for the pendulum system the PINNs outperformed equivalent uninformed neural networks (NNs) in the ideal data case, with accuracy improvements of 18x and 6x for 10 linearly-spaced and 10 uniformly-distributed random training points respectively. In similar test cases with real data collected from an experiment, PINNs outperformed NNs with 9.3x and 9.1x accuracy improvements for 67 linearly-spaced and uniformly-distributed random points respectively. For the 2D heat diffusion, we show that both PINNs and NNs do not fare very well in reconstructing the heating regime due to difficulties in optimizing the network parameters over a large domain in both time and space. We highlight that data denoising and smoothing, reducing the size of the optimization problem, and using LBFGS as the optimizer are all ways to improve the accuracy of the predicted solution for both PINNs and NNs. Additionally, we address the viability of deploying physics-informed models within physical systems, and we choose FPGAs as the compute substrate for deployment. In light of this, we perform our experiments using a PYNQ-Z1 FPGA and identify issues related to time-coherent sensing and spatial data alignment. We discuss the insights gained from this work and list future work items based on the proposed architecture for the system that our methods work to develop.

Related papers

• Neuromorphic Wireless Split Computing with Multi-Level Spikes [69.73249913506042]
  In neuromorphic computing, spiking neural networks (SNNs) perform inference tasks, offering significant efficiency gains for workloads involving sequential data. Recent advances in hardware and software have demonstrated that embedding a few bits of payload in each spike exchanged between the spiking neurons can further enhance inference accuracy. This paper investigates a wireless neuromorphic split computing architecture employing multi-level SNNs.
  arXiv  Detail & Related papers  (2024-11-07T14:08:35Z)
• Transformer neural networks and quantum simulators: a hybrid approach for simulating strongly correlated systems [1.6494451064539348]
  We present a hybrid optimization scheme for neural quantum states (NQS) that involves a data-driven pretraining with numerical or experimental data and a second, Hamiltonian-driven optimization stage. Our work paves the way for a reliable and efficient optimization of neural quantum states.
  arXiv  Detail & Related papers  (2024-05-31T17:55:27Z)
• Assessing Neural Network Representations During Training Using Noise-Resilient Diffusion Spectral Entropy [55.014926694758195]
  Entropy and mutual information in neural networks provide rich information on the learning process. We leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. We show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data.
  arXiv  Detail & Related papers  (2023-12-04T01:32:42Z)
• On-Sensor Data Filtering using Neuromorphic Computing for High Energy Physics Experiments [1.554920942634392]
  We present our approach for developing a compact neuromorphic model that filters out the sensor data based on the particle's transverse momentum. The incoming charge waveforms are converted to streams of binary-valued events, which are then processed by the SNN.
  arXiv  Detail & Related papers  (2023-07-20T21:25:25Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• MAgNet: Mesh Agnostic Neural PDE Solver [68.8204255655161]
  Climate predictions require fine-temporal resolutions to resolve all turbulent scales in the fluid simulations. Current numerical model solveers PDEs on grids that are too coarse (3km to 200km on each side) We design a novel architecture that predicts the spatially continuous solution of a PDE given a spatial position query.
  arXiv  Detail & Related papers  (2022-10-11T14:52:20Z)
• Auto-PINN: Understanding and Optimizing Physics-Informed Neural Architecture [77.59766598165551]
  Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. Here, we propose Auto-PINN, which employs Neural Architecture Search (NAS) techniques to PINN design. A comprehensive set of pre-experiments using standard PDE benchmarks allows us to probe the structure-performance relationship in PINNs.
  arXiv  Detail & Related papers  (2022-05-27T03:24:31Z)
• Adaptive Anomaly Detection for Internet of Things in Hierarchical Edge Computing: A Contextual-Bandit Approach [81.5261621619557]
  We propose an adaptive anomaly detection scheme with hierarchical edge computing (HEC) We first construct multiple anomaly detection DNN models with increasing complexity, and associate each of them to a corresponding HEC layer. Then, we design an adaptive model selection scheme that is formulated as a contextual-bandit problem and solved by using a reinforcement learning policy network.
  arXiv  Detail & Related papers  (2021-08-09T08:45:47Z)
• Learning Functional Priors and Posteriors from Data and Physics [3.537267195871802]
  We develop a new framework based on deep neural networks to be able to extrapolate in space-time using historical data. We employ the physics-informed Generative Adversarial Networks (PI-GAN) to learn a functional prior. At the second stage, we employ the Hamiltonian Monte Carlo (HMC) method to estimate the posterior in the latent space of PI-GANs.
  arXiv  Detail & Related papers  (2021-06-08T03:03:24Z)
• Physics-aware deep neural networks for surrogate modeling of turbulent natural convection [0.0]
  We investigate the use of PINNs surrogate modeling for turbulent Rayleigh-B'enard convection flows. We show how it comes to play as a regularization close to the training boundaries which are zones of poor accuracy for standard PINNs. The predictive accuracy of the surrogate over the entire half a billion DNS coordinates yields errors for all flow variables ranging between [0.3% -- 4%] in the relative L 2 norm.
  arXiv  Detail & Related papers  (2021-03-05T09:48:57Z)
• Multi-fidelity Bayesian Neural Networks: Algorithms and Applications [0.0]
  We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity. We apply them to learn function approximations as well as to solve inverse problems based on partial differential equations (PDEs)
  arXiv  Detail & Related papers  (2020-12-19T02:03:53Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.