Recent Advances in Physics-Informed Machine Learning

Dear Colleagues,

Physics-informed machine learning (PIML) is rapidly emerging as a powerful paradigm for integrating data-driven learning with fundamental physical principles. By incorporating prior knowledge such as governing equations, conservation laws, symmetries, constitutive relationships, and physical constraints into machine learning, PIML can improve data efficiency, interpretability, robustness, and generalization while providing new computational tools for modeling complex physical and biological systems.

This Special Issue highlights recent methodological advances and emerging applications in physics-informed machine learning. Topics of particular interest include physics-informed neural networks, scientific machine learning, neural operators, differentiable physics, hybrid mechanistic–machine learning models, and other approaches that integrate physical knowledge with modern machine learning architectures. We welcome both theoretical and computational contributions that advance the foundations, scalability, accuracy, and reliability of these methods.

Beyond incorporating known physical principles, machine learning is increasingly being used for the data-driven discovery of governing equations, constitutive relationships, and hidden physical mechanisms. Approaches such as symbolic regression, sparse identification, operator learning, and data-driven model discovery offer new opportunities to extract interpretable scientific knowledge from experimental and observational data.

Emerging applications further extend PIML toward digital twins and physical AI. Physics-informed models can support real-time representations of physical systems, learning-based control, robotics, autonomous systems, and intelligent decision-making. The integration of machine learning and physical modeling is similarly creating new opportunities across engineering, physical sciences, and biological and biomedical systems, ranging from fluid and solid mechanics, materials, energy, and climate science to molecular modeling, biomechanics, physiological systems, and computational biology.

This Special Issue aims to bring together research from the fields of machine learning, computational science, applied mathematics, engineering, and physical and life sciences to present recent advances in the foundations and applications of physics-informed machine learning.

Topics of interest include the following:

• Physics-informed and physics-guided machine learning.
• Scientific machine learning.
• Physics-informed neural networks (PINNs).
• Neural operators and operator learning.
• Hybrid mechanistic and machine learning models.
• Differentiable physics and differentiable simulation.
• AI for scientific discovery and equation discovery.
• Surrogate and reduced-order modeling.
• AI-accelerated scientific simulation.
• Inverse problems and parameter estimation.
• Multiscale and multiphysics modeling.
• Digital twins.
• Physics-informed reinforcement learning and control.
• Physical AI, robotics, and autonomous systems.
• Scientific and engineering design and optimization.
• Uncertainty quantification and probabilistic modeling.
• Robustness, interpretability, and trustworthy scientific AI.
• Applications in engineering, physical sciences, and biological and biomedical systems.

Dr. Yixiang Deng
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the Special Issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Publisher’s Notice

Following discussions between the Journal Algorithms Editorial Office and the Guest Editor, the Special Issue description has been revised. This change has been approved by the journal Editorial Board, and the Special Issue website has been updated accordingly on 25 August 2026. The Special Issue will continue to be handled by the Guest Editor in accordance with MDPI’s Special Issue and editorial policies.