AI and Generative Modeling for Inverse Problems in Science and Engineering

Dear Colleagues,

Inverse problems play a central role in many areas of science and engineering, ranging from medical imaging and geophysics to climate modeling, materials science, and fluid dynamics. These problems are notoriously difficult to resolve. They are often ill-posed, data may be scarce or noisy, and the underlying physics can make computations extremely demanding. In recent years, advances in artificial intelligence and machine learning have begun to change the way in which we approach inverse problems, offering new tools that are faster, more flexible, and increasingly grounded in physical principles.

A growing area of scientific machine learning is focused on bringing physics and learning together. Physics-informed neural networks (PINNs) and Fourier neural operators (FNOs) provide ways to accelerate forward solvers and embed physical laws directly into the learning process. At the same time, generative models, such as diffusion models, flow matching, and invertible neural networks, are proving powerful for sampling complex solution spaces, capturing uncertainties, and regularizing inverse problems. These approaches are not only helping us to solve problems more efficiently but also deepening our understanding of how AI and physics can work hand in hand.

This Special Issue will highlight the latest advances at the intersection of AI, machine learning, and inverse problems. We are particularly interested in contributions that demonstrate how physics-guided learning, generative models, and operator-based approaches can push the boundaries of what is possible in both theory and practice. We welcome both original research papers and comprehensive reviews.

Topics of interest include (but are not limited to) the following:

• Physics-guided machine learning for inverse problems: physics-informed neural networks (PINNs), Fourier neural operators (FNOs), and hybrid methods combining data and physical laws;
• Generative AI for inverse problems: diffusion models, flow matching, invertible neural networks, and probabilistic generative models;
• Forward problem acceleration: machine learning surrogates for PDE solvers, reduced-order models, multi-scale simulation, and uncertainty quantification;
• Theoretical foundations: generalization, stability, interpretability, and convergence guarantees in physics-informed and scientific machine learning;
• Applications across science and engineering: imaging, geophysics, climate science, materials design, fluid dynamics, medical diagnostics, etc.;
• Emerging directions: self-supervised and unsupervised methods for sparse, noisy, multimodal, or multi-fidelity data, as well as methods for few-shot and data-efficient experimental design.

By bringing together diverse contributions, this Special Issue will showcase how AI and machine learning are reshaping the study of inverse problems and creating new opportunities for scientific discovery.

Dr. Xuqing Wu
Guest Editor

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• inverse problems
• scientific machine learning
• physics-informed neural networks (PINNs)
• neural operators
• generative models
• normalizing flows
• invertible neural networks
• uncertainty quantification
• surrogate model
• computational imaging