Physics-Based Models

Defining and Describing Physics-Based Models

Uses in Context

• In engineering, “physics-based modeling” commonly describes simulations that predict system behavior from mechanics, thermodynamics, fluid dynamics, electromagnetism, or other established laws rather than from statistical correlations alone.[13]
• In scientific machine learning, “physics-informed” describes neural networks whose training is constrained by physical laws; this approach is used for forward simulation and inverse problems involving nonlinear partial differential equations.[1][4]
• In digital-twin research, physics-informed models are used to connect computational representations of engineered systems with sensor data and operational behavior.[2]
• In education, model-based reasoning treats a model as a representation of a real-world system designed to support explanation, understanding, prediction, or investigation.[13]
• In product and design work, the term can signal that a virtual prototype is intended to preserve physically meaningful relationships, rather than merely imitate observed outputs.[13]

History of Use

Origins

• The underlying practice predates the modern label: scientific modeling developed as a way to represent physical systems through theories, mathematical relationships, and idealizations. One account defines a scientific model as a conceptual system mapped onto the structure or behavior of physical systems so that it can reliably represent a relevant pattern and serve a purpose.[13]
• In computational science, physics-based modeling became associated with numerical solutions of governing equations, including partial differential equations used to represent fields, flows, structures, and other continuously varying systems.[4]
• The modern machine-learning expression physics-informed neural networks was introduced by Maziar Raissi, Paris Perdikaris, and George Em Karniadakis in a 2019 Journal of Computational Physics paper titled “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.”[1][4]

Evolution

• Before the 2010s — equation-based simulation: Physics-based models were primarily constructed from mechanistic equations and solved with numerical methods. Their principal strengths were interpretability and physical consistency, while their limitations included computational cost and dependence on accurate parameters and boundary conditions.[13]
• 2019 — physics-informed learning: Raissi, Perdikaris, and Karniadakis formalized a neural-network framework that embeds physical laws into learning and applies it to forward and inverse nonlinear partial-differential-equation problems.[1][4]
• 2020s — hybrid models and digital twins: Research increasingly combined physics-based representations with neural networks, sensor data, and digital-twin architectures. Recent literature describes physics-informed neural methods as a route for engineering digital twins and computational mechanics.[2][9]

Best Real-World Examples

• Physics-informed neural networks — neural networks constrained by governing equations for forward simulation and inverse discovery.[1][4]
• Model-Based Reasoning in the Upper-Division Physics Laboratory — an educational example of using models to explain, understand, and predict physical phenomena.[13]
• Physics-informed digital twins — hybrid engineering systems that combine physical models with neural networks and operational data.[2]
• Physics-informed computational mechanics — applications of physics-informed methods to mechanics problems involving fields, forces, and material behavior.[9]
• Physics-driven convolutional operators — research exploring neural architectures designed around physical structure rather than treating physics solely as an external training constraint.[11]
• Physics-informed field reconstruction — reconstruction of unobserved physical fields by combining measurements with physical constraints.[10]

Case Studies

Sources