Explainable Physics-Informed Machine Learning: A Review and Comparative Assessment of Methods

Supervisors: Christoforos Rekatsinas, Vasilis Gkatsis

Description:

Modern machine learning methods have shown strong potential in physics and engineering problems, but their use in scientific domains is often limited by data scarcity, poor interpretability, and weak guarantees of physical consistency. Physics-informed machine learning addresses these limitations by embedding prior knowledge into the learning process, including governing equations, conservation laws, boundary conditions, symmetry constraints, expert rules, or simulation-based knowledge. Although these models are often presented as more interpretable than purely data-driven approaches, the degree and usefulness of their explainability remain open questions.
This thesis will focus mainly on a structured review of explainable physics-informed machine learning methods. The student will study and classify approaches such as Physics-Informed Neural Networks, Physics-Guided Neural Networks, Neural Operators with physical constraints, hybrid physics–ML models, symbolic regression, sparse identification of governing equations, and neuro-symbolic methods. The review will cover approximately 80–90 scientific references and will organize the literature according to the type of physical knowledge used, the target application, the level of interpretability, and the explainability technique employed.
A limited implementation component will also be included. The student will reproduce or develop simple benchmark examples to compare selected methods in terms of accuracy, data efficiency, physical consistency, and explainability. Possible test cases may include simple dynamical systems, diffusion-type equations, or low-dimensional mechanics problems. The objective is not to develop a new large-scale model, but to provide a critical and well-structured assessment of how explainable physics-informed machine learning methods can be evaluated and compared.

Qualifications required: Python programming; Machine Learning and Deep Learning algorithms