计算物理：2025–2026 年度综述

An annual survey of the physics.comp-ph arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 120 papers and organised into 44 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• GPU-Accelerated Multiphysics Co-Simulation for Advanced Engineering Design (48.4%) — This subdirection focuses on developing full-scale, GPU-accelerated co-simulation frameworks that couple electromagnetic, thermal, and mechanical physics for early-stage design of advanced packages and systems.
• Machine Learning Surrogates and Differentiable Solvers for Physical PDEs (31.1%) — This subdirection addresses accelerating transient PDE solvers and learning nonlinear dynamics via online-learned preconditioners, symbolic regression, and differentiable simulation frameworks.
• Density Functional Theory and Electronic Structure of Correlated Materials (8.9%) — This subdirection investigates electronic, structural, and magnetic properties of materials through density functional theory and related many-body methods, focusing on correlated and functional materials.
• Quantum Monte Carlo and Tensor Network Methods for Many-Body Systems (4.4%) — This subdirection develops scalable quantum Monte Carlo and tensor network algorithms to compute ground states, transport properties, and quantum dynamics of strongly correlated many-body systems.
• Kinetic Plasma and Lattice Boltzmann Methods for Multiscale Fluid Dynamics (3.4%) — This subdirection advances numerical schemes for kinetic plasma, lattice Boltzmann, and hydrodynamic simulations, addressing turbulence, particle interactions, and phase-change flows across scales.
• Phase Transition Prediction and Machine Learning for Materials Synthesis (1.5%) — This subdirection tackles predicting phase transitions and critical phenomena in materials, leveraging machine learning and physics-informed neural networks to guide synthesis and processing.
• Finite Element and Boundary Integral Methods for Complex Geometries (1.3%) — This subdirection develops stabilized finite element and boundary integral formulations for complex geometries, including curvilinear surfaces, periodic composites, and moving boundaries.
• Data-Driven Optical and Quantum Control for Extreme Field Interactions (0.8%) — This subdirection applies data-driven techniques and structured light control to high-field laser-matter interactions, quantum optics, and precision measurement in chemistry and engineering.
• Dynamical Mean-Field Theory and Vortex Shedding in Complex Flows (0.1%) — This subdirection examines dynamical phenomena governed by continuous mechanisms, including bath fitting for DMFT and vortex shedding from moving plates in viscous and inviscid regimes.
• Homotopy Continuation and Robust Numerical Methods for Waveguide Dispersion (0.1%) — This subdirection develops robust homotopy continuation and finite-precision numerical techniques for computing viscoelastic waveguide dispersion curves and probability tables in resonance self-shielding.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.