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

• URL: http://arxiv.org/abs/2501.18708v2
• Date: Wed, 02 Apr 2025 18:37:59 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: SciML is a research field which combines physics-based and data-driven models.<n>Data-driven models aim to extract relations between input and output data.<n>We discuss the successful application of SciML to the simulation of the human cardiac function.
• Score: 3.912796219404492
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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, 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, increasingly cheap computing power, and the development of powerful ML algorithms. SciML leverages the physical awareness of physics-based models and the efficiency of data-driven algorithms. With SciML, we can inject physics and mathematical knowledge into ML algorithms. Yet, we can rely on data-driven algorithms' capability to discover complex and nonlinear patterns from data and improve the descriptive capacity of physics-based models. After recalling the mathematical foundations of digital modelling and ML algorithms and presenting the most popular ML architectures, we discuss the great potential of a broad variety of SciML strategies in solving complex problems governed by PDEs. Finally, we illustrate the successful application of SciML to the simulation of the human cardiac function, a field of significant socioeconomic importance that poses numerous challenges on both the mathematical and computational fronts. 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

• Machine learning for modelling unstructured grid data in computational physics: a review [37.19820094095164]
  Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. This review is intended as a guidebook for computational scientists seeking to apply machine learning approaches to unstructured grid data. It places special focus on how ML methods can overcome the inherent limitations of traditional numerical techniques. Emerging directions such as generative models with unstructured data, reinforcement learning for mesh generation, and hybrid physics-data-driven paradigms are discussed.
  arXiv  Detail & Related papers  (2025-02-13T14:11:33Z)
• Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics [5.5371760658918]
  Integration of deep learning techniques and physics-driven designs is reforming the way we address inverse problems. This perspective highlights advances and potential of physics-driven learning methods. It is shown that the fusion of ML and physics can lead to more efficient and reliable problem-solving strategies.
  arXiv  Detail & Related papers  (2025-01-09T21:14:25Z)
• Replication Study: Enhancing Hydrological Modeling with Physics-Guided Machine Learning [0.0]
  Current hydrological modeling methods combine data-driven Machine Learning algorithms and traditional physics-based models. Despite the accuracy of ML in outcome prediction, the integration of scientific knowledge is crucial for reliable predictions. This study introduces a Physics Informed Machine Learning model, which merges the process understanding of conceptual hydrological models with the predictive efficiency of ML algorithms.
  arXiv  Detail & Related papers  (2024-02-21T16:26:59Z)
• 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)
• Learning Controllable Adaptive Simulation for Multi-resolution Physics [86.8993558124143]
  We introduce Learning controllable Adaptive simulation for Multi-resolution Physics (LAMP) as the first full deep learning-based surrogate model. LAMP consists of a Graph Neural Network (GNN) for learning the forward evolution, and a GNN-based actor-critic for learning the policy of spatial refinement and coarsening. We demonstrate that our LAMP outperforms state-of-the-art deep learning surrogate models, and can adaptively trade-off computation to improve long-term prediction error.
  arXiv  Detail & Related papers  (2023-05-01T23:20:27Z)
• 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)<n>MINN learns the physics-based dynamics of general autonomous or non-autonomous systems consisting of partial differential-algebraic equations (PDAEs)<n>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)
• 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)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• 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)
• Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes [1.0635248457021496]
  We develop a Physics Informed Machine Learning (PIML) model that combines the process understanding of conceptual hydrological model with predictive abilities of state-of-the-art ML models. We apply the proposed model to predict the monthly time series of the target (streamflow) and intermediate variables (actual evapotranspiration) in the Narmada river basin in India.
  arXiv  Detail & Related papers  (2021-04-22T12:13:42Z)
• 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.