pbdl book

The book addresses how neural networks can be trained to learn physics simulations, accelerate numerical solvers, incorporate physical constraints as loss terms, and generate solutions to partial differential equations through physics-informed machine learning approaches.

The content progresses from fundamental conceptshow neural networks represent physical fields, how automatic differentiation enables physics-based loss termsthrough advanced topics including physics-informed neural networks (PINNs), neural operators like Fourier Neural Operator and DeepONet, differentiable physics simulators, and learned turbulence closure models.

Each chapter is paired with runnable Jupyter notebooks implementing the discussed methods, enabling readers to build hands-on intuition for when different approaches work and where they break down.

Graduate students in computational science and engineering, ML researchers extending into scientific computing, and domain scientists (physicists, engineers, climate scientists) looking to apply deep learning to simulation acceleration use PBDL Book as a structured introduction to this interdisciplinary area.

The open-access format removes textbook cost barriers, and executable notebooks lower the threshold from reading to experimentation.

Commercial applications in drug discovery, materials design, and numerical weather prediction have made resources bridging physics and ML increasingly valuable for practitioners across both communities.