Learning governing physics from output only measurements

• URL: http://arxiv.org/abs/2208.05609v1
• Date: Thu, 11 Aug 2022 02:24:03 GMT
• Title: Learning governing physics from output only measurements
• Authors: Tapas Tripura and Souvik Chakraborty
• Abstract summary: We propose a novel framework for learning governing physics of dynamical system from output only measurements. In particular, we combine sparsity promoting spike and slab prior, Bayes law, and Euler Maruyama scheme to identify the governing physics from data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Extracting governing physics from data is a key challenge in many areas of science and technology. The existing techniques for equations discovery are dependent on both input and state measurements; however, in practice, we only have access to the output measurements only. We here propose a novel framework for learning governing physics of dynamical system from output only measurements; this essentially transfers the physics discovery problem from the deterministic to the stochastic domain. The proposed approach models the input as a stochastic process and blends concepts of stochastic calculus, sparse learning algorithms, and Bayesian statistics. In particular, we combine sparsity promoting spike and slab prior, Bayes law, and Euler Maruyama scheme to identify the governing physics from data. The resulting model is highly efficient and works with sparse, noisy, and incomplete output measurements. The efficacy and robustness of the proposed approach is illustrated on several numerical examples involving both complete and partial state measurements. The results obtained indicate the potential of the proposed approach in identifying governing physics from output only measurement.

Related papers

• Physics-Informed Variational State-Space Gaussian Processes [23.57905861783904]
  We introduce a variational-temporal state-temporal GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.
  arXiv  Detail & Related papers  (2024-09-20T20:12:11Z)
• Predicting Probabilities of Error to Combine Quantization and Early Exiting: QuEE [68.6018458996143]
  We propose a more general dynamic network that can combine both quantization and early exit dynamic network: QuEE. Our algorithm can be seen as a form of soft early exiting or input-dependent compression. The crucial factor of our approach is accurate prediction of the potential accuracy improvement achievable through further computation.
  arXiv  Detail & Related papers  (2024-06-20T15:25:13Z)
• Learning the solution operator of two-dimensional incompressible Navier-Stokes equations using physics-aware convolutional neural networks [68.8204255655161]
  We introduce a technique with which it is possible to learn approximate solutions to the steady-state Navier--Stokes equations in varying geometries without the need of parametrization. The results of our physics-aware CNN are compared to a state-of-the-art data-based approach.
  arXiv  Detail & Related papers  (2023-08-04T05:09:06Z)
• Physics-informed Information Field Theory for Modeling Physical Systems with Uncertainty Quantification [0.0]
  Information field theory (IFT) provides the tools necessary to perform statistics over fields that are not necessarily Gaussian. We extend IFT to physics-informed IFT (PIFT) by encoding the functional priors with information about the physical laws which describe the field. The posteriors derived from this PIFT remain independent of any numerical scheme and can capture multiple modes. We numerically demonstrate that the method correctly identifies when the physics cannot be trusted, in which case it automatically treats learning the field as a regression problem.
  arXiv  Detail & Related papers  (2023-01-18T15:40:19Z)
• Learning new physics efficiently with nonparametric methods [11.970219534238444]
  We present a machine learning approach for model-independent new physics searches. The corresponding algorithm is powered by recent large-scale implementations of kernel methods. We show that our approach has dramatic advantages compared to neural network implementations in terms of training times and computational resources.
  arXiv  Detail & Related papers  (2022-04-05T16:17:59Z)
• DeepPhysics: a physics aware deep learning framework for real-time simulation [0.0]
  We propose a solution to simulate hyper-elastic materials using a data-driven approach. A neural network is trained to learn the non-linear relationship between boundary conditions and the resulting displacement field. The results show that our network architecture trained with a limited amount of data can predict the displacement field in less than a millisecond.
  arXiv  Detail & Related papers  (2021-09-17T12:15:47Z)
• An Extensible Benchmark Suite for Learning to Simulate Physical Systems [60.249111272844374]
  We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time-based and representative data-driven methods.
  arXiv  Detail & Related papers  (2021-08-09T17:39:09Z)
• Hessian-based toolbox for reliable and interpretable machine learning in physics [58.720142291102135]
  We present a toolbox for interpretability and reliability, extrapolation of the model architecture. It provides a notion of the influence of the input data on the prediction at a given test point, an estimation of the uncertainty of the model predictions, and an agnostic score for the model predictions. Our work opens the road to the systematic use of interpretability and reliability methods in ML applied to physics and, more generally, science.
  arXiv  Detail & Related papers  (2021-08-04T16:32:59Z)
• Simultaneous boundary shape estimation and velocity field de-noising in Magnetic Resonance Velocimetry using Physics-informed Neural Networks [70.7321040534471]
  Magnetic resonance velocimetry (MRV) is a non-invasive technique widely used in medicine and engineering to measure the velocity field of a fluid. Previous studies have required the shape of the boundary (for example, a blood vessel) to be known a priori. We present a physics-informed neural network that instead uses the noisy MRV data alone to infer the most likely boundary shape and de-noised velocity field.
  arXiv  Detail & Related papers  (2021-07-16T12:56:09Z)
• Neural network quantum state tomography in a two-qubit experiment [52.77024349608834]
  Machine learning inspired variational methods provide a promising route towards scalable state characterization for quantum simulators. We benchmark and compare several such approaches by applying them to measured data from an experiment producing two-qubit entangled states. We find that in the presence of experimental imperfections and noise, confining the variational manifold to physical states greatly improves the quality of the reconstructed states.
  arXiv  Detail & Related papers  (2020-07-31T17:25:12Z)
• Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem [0.0]
  We present a new hybrid physics-based machine-learning approach to reservoir modeling. The methodology relies on a series of deep adversarial neural network architecture with physics-based regularization. The proposed methodology is a simple and elegant way to instill physical knowledge to machine-learning algorithms.
  arXiv  Detail & Related papers  (2020-01-15T08:20:11Z)

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.