Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning

• URL: http://arxiv.org/abs/2501.18708v1
• Date: Thu, 30 Jan 2025 19:09:38 GMT
• Title: Combining physics-based and data-driven models: advancing the frontiers of research with Scientific Machine Learning
• Authors: Alfio Quarteroni, Paola Gervasio, Francesco Regazzoni,
• Abstract summary: Machine learning combines physics-based and data-driven models. With SciML, we can inject physics and mathematical knowledge into machine learning algorithms. We discuss the great potential of a broad variety of SciML strategies in solving complex problems governed by partial differential equations.
• Score: 3.912796219404492
• License:
• Abstract: Scientific Machine Learning (SciML) is a recently emerged research field which combines physics-based and data-driven models for the numerical approximation of differential problems. Physics-based models rely on the physical understanding of the problem at hand, subsequent mathematical formulation, and numerical approximation. Data-driven models instead aim to extract relations between input and output data without arguing any causality principle underlining the available data distribution. In recent years, data-driven models have been rapidly developed and popularized. Such a diffusion has been triggered by a huge availability of data (the so-called big data), an increasingly cheap computing power, and the development of powerful machine learning algorithms. SciML leverages the physical awareness of physics-based models and, at the same time, the efficiency of data-driven algorithms. With SciML, we can inject physics and mathematical knowledge into machine learning algorithms. Yet, we can rely on data-driven algorithms' capability to discover complex and non-linear patterns from data and improve the descriptive capacity of physics-based models. After recalling the mathematical foundations of digital modelling and machine learning algorithms, and presenting the most popular machine learning architectures, we discuss the great potential of a broad variety of SciML strategies in solving complex problems governed by partial differential equations. Finally, we illustrate the successful application of SciML to the simulation of the human cardiac function, a field of significant socio-economic importance that poses numerous challenges on both the mathematical and computational fronts. The corresponding mathematical model is a complex system of non-linear ordinary and partial differential equations describing the electromechanics, valve dynamics, blood circulation, perfusion in the coronary tree, and torso potential. Despite the robustness and accuracy of physics-based models, certain aspects, such as unveiling constitutive laws for cardiac cells and myocardial material properties, as well as devising efficient reduced order models to dominate the extraordinary computational complexity, have been successfully tackled by leveraging data-driven models.

Related papers

• Mechanistic Neural Networks for Scientific Machine Learning [58.99592521721158]
  We present Mechanistic Neural Networks, a neural network design for machine learning applications in the sciences. It incorporates a new Mechanistic Block in standard architectures to explicitly learn governing differential equations as representations. Central to our approach is a novel Relaxed Linear Programming solver (NeuRLP) inspired by a technique that reduces solving linear ODEs to solving linear programs.
  arXiv  Detail & Related papers  (2024-02-20T15:23:24Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling [2.1303885995425635]
  We propose a novel machine learning architecture, termed model-integrated neural networks (MINN) MINN learns the physics-based dynamics of general autonomous or non-autonomous systems consisting of partial differential-algebraic equations (PDAEs) We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries.
  arXiv  Detail & Related papers  (2023-04-27T09:11:40Z)
• Neural Operator: Is data all you need to model the world? An insight into the impact of Physics Informed Machine Learning [13.050410285352605]
  We provide an insight into how data-driven approaches can complement conventional techniques to solve engineering and physics problems. We highlight a novel and fast machine learning-based approach to learning the solution operator of a PDE operator learning.
  arXiv  Detail & Related papers  (2023-01-30T23:29:33Z)
• Advancing Reacting Flow Simulations with Data-Driven Models [50.9598607067535]
  Key to effective use of machine learning tools in multi-physics problems is to couple them to physical and computer models. The present chapter reviews some of the open opportunities for the application of data-driven reduced-order modeling of combustion systems.
  arXiv  Detail & Related papers  (2022-09-05T16:48:34Z)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Model-Based Deep Learning [155.063817656602]
  Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Deep neural networks (DNNs) use generic architectures which learn to operate from data, and demonstrate excellent performance. We are interested in hybrid techniques that combine principled mathematical models with data-driven systems to benefit from the advantages of both approaches.
  arXiv  Detail & Related papers  (2020-12-15T16:29:49Z)
• Data-Efficient Learning for Complex and Real-Time Physical Problem Solving using Augmented Simulation [49.631034790080406]
  We present a task for navigating a marble to the center of a circular maze. We present a model that learns to move a marble in the complex environment within minutes of interacting with the real system.
  arXiv  Detail & Related papers  (2020-11-14T02:03:08Z)
• Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics [3.214927790437842]
  Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. Our findings are of interest for model-based control and system identification of mechanical systems.
  arXiv  Detail & Related papers  (2020-05-29T15:10:43Z)

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.