🧮 Scientific Computing¶

🤖 AAAI2026 · 8 paper notes

Just Few States are Enough: Randomized Sparse Feedback for Stability of Dynamical Systems: This paper proposes a randomized sparse feedback control framework in which the controller accesses only a random subset of the state vector at each time step. Feedback gain matrices and Bernoulli sparsification parameters are jointly designed via LMIs to guarantee asymptotic mean-square stability (AMSS) while minimizing the required number of active sensors. Experiments demonstrate that as few as 0.3% of state components suffice to achieve performance comparable to full-state feedback.
Knowledge-Guided Masked Autoencoder with Linear Spectral Mixing and Spectral-Angle-Aware Reconstruction: This paper proposes KARMA, a framework that embeds the Linear Spectral Mixing Model (LSMM) as a physics constraint within the ViT-MAE decoder, combined with a Spectral Angle Mapper (SAM) loss, to improve reconstruction fidelity and downstream transfer performance for hyperspectral remote sensing imagery.
Phys-Liquid: A Physics-Informed Dataset for Estimating 3D Geometry and Volume of Transparent Deformable Liquids: This work introduces the Phys-Liquid dataset (97,200 physics-simulated images with 3D meshes), which models dynamic deformation of liquids inside transparent containers based on the Navier-Stokes equations, and proposes a four-stage reconstruction pipeline (segmentation → multi-view mask generation → 3D reconstruction → scaling) to achieve high-accuracy liquid geometry and volume estimation in both simulated and real-world scenes.
PhysicsCorrect: A Training-Free Approach for Stable Neural PDE Simulations: This paper proposes PhysicsCorrect, a training-free correction framework that models PDE residual correction as a linearized inverse problem and precomputes a cached pseudoinverse. At inference time, it achieves up to 100× error reduction with less than 5% computational overhead, and is applicable to arbitrary pretrained neural operators including FNO, UNet, and ViT.
PIMRL: Physics-Informed Multi-Scale Recurrent Learning for Burst-Sampled Spatiotemporal Dynamics: This paper proposes PIMRL, a framework for learning from burst-sampled (short high-frequency bursts followed by long intervals) sparse spatiotemporal data. It features a dual-module architecture combining macro-scale latent-space reasoning and micro-scale physics correction, integrated via cross-scale message passing, achieving up to 80% error reduction across 5 PDE benchmarks.
SAOT: An Enhanced Locality-Aware Spectral Transformer for Solving PDEs: This paper proposes SAOT (Spectral Attention Operator Transformer), which captures high-frequency local details via linear-complexity Wavelet Attention (WA) and complements it with the global receptive field of Fourier Attention (FA) through a gated fusion mechanism. SAOT achieves state-of-the-art performance on 6 operator learning benchmarks, reducing the relative error on Navier-Stokes by 22.3% compared to Transolver.
Scientific Knowledge-Guided Machine Learning for Vessel Power Prediction: A Comparative Study: A hybrid modeling framework combining a physics baseline with a data-driven residual is proposed. The sea trial power curve (propeller law \(P=cV^n\)) serves as the baseline, and XGBoost/NN/PINN models learn the residual correction, significantly improving extrapolation stability and physical consistency in sparse data regions.
Towards a Foundation Model for Partial Differential Equations Across Physics Domains: This paper proposes PDE-FM, a modular PDE foundation model combining spatial-spectral dual-modal tokenization, FiLM-based physics modulation, and a Mamba state-space backbone. It achieves an average 46% reduction in VRMSE across 12 heterogeneous physics-domain datasets from The Well benchmark.