🧮 Scientific Computing¶

🔬 ICLR2026 · 10 paper notes

Astral: Training Physics-Informed Neural Networks with Error Majorants: This paper proposes the Astral loss function — based on a functional a posteriori error majorant — as a replacement for the conventional residual loss in training physics-informed neural networks (PiNNs). The approach enables reliable error estimation throughout training and achieves superior or comparable accuracy across multiple PDE types, including diffusion and Maxwell equations.
Deep Learning for Subspace Regression: This paper formalizes the subspace prediction problem in Reduced Order Modeling (ROM) as a regression task on the Grassmann manifold. It proposes dedicated loss functions and a subspace embedding technique—predicting a higher-dimensional subspace containing the target—to reduce mapping complexity. The approach achieves significant improvements across eigenvalue problems, parametric PDEs, and iterative solver acceleration.
DGNet: Discrete Green Networks for Data-Efficient Learning of Spatiotemporal PDEs: Grounded in Green's function theory, DGNet embeds the superposition principle into a physics-neural hybrid architecture, achieving state-of-the-art accuracy with only tens of training trajectories and demonstrating robust zero-shot generalization to unseen source terms.
DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning: DRIFT-Net is a dual-branch neural operator that addresses autoregressive drift caused by insufficient global spectral coupling in window attention, via controlled low-frequency mixing (spectral branch), local detail fidelity (image branch), and bandwidth fusion through radial gating. It reduces error by 7%–54% on Navier-Stokes benchmarks.
Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discovery: This paper systematically evaluates vanilla KAN as a drop-in replacement for MLP in the residual branch of Hard-Constrained Recurrent Physics-Informed Neural Networks (HRPINN) — through 3 complementary studies × 100 random seeds, it finds that KAN is competitive on univariate separable residuals (Duffing's \(-0.3x^3\)), but systematically fails on multiplicatively coupled residuals (Van der Pol's \((1-x^2)v\)) with extreme hyperparameter fragility, while standard MLP exhibits substantially superior stability across nearly all configurations.
HyperKKL: Enabling Non-Autonomous State Estimation through Dynamic Weight Conditioning: This paper proposes HyperKKL, which uses a hypernetwork to encode exogenous input signals and dynamically generate the transformation mapping parameters of a KKL observer, enabling state estimation for non-autonomous nonlinear systems without retraining or online gradient updates. The method is validated on four classical nonlinear systems: Duffing, Van der Pol, Lorenz, and Rössler.
Learning-guided Kansa Collocation for Forward and Inverse PDE Problems: This work extends the meshfree radial basis function (RBF)-based Kansa collocation method from single-variable linear PDEs to coupled multi-variable and nonlinear PDE settings. It incorporates automatic shape-parameter tuning and multiple time-stepping schemes, and provides a systematic comparison against neural PDE solvers such as PINNs and FNO on both forward and inverse problems.
One Operator to Rule Them All? On Boundary-Indexed Operator Families in Neural PDE Solvers: This paper argues that neural PDE solvers, when trained under varying boundary conditions, do not learn a single solution operator but rather a family of operators indexed by boundary conditions. It formalizes the non-identifiability problem induced by boundary distribution shift under ERM from a learning-theoretic perspective.
Policy Myopia as a Mechanism of Gradual Disempowerment in Post-AGI Governance: This paper argues that policy myopia is not an attention-allocation problem but an institutional mechanism that systematically and irreversibly strips humans of governance participation capacity in the post-AGI era — through three coupled positive feedback loops: salience capture, capability cascades, and value lock-in. Standard mitigation measures can only delay but not prevent this process.
Supervised Metric Regularization Through Alternating Optimization for Multi-Regime PINNs: This paper proposes a Topology-Aware PINN (TAPINN) that structures the latent space via supervised metric regularization (Triplet Loss) and stabilizes training through an alternating optimization schedule. On the multi-regime Duffing oscillator benchmark, TAPINN reduces physics residuals by approximately 49% (0.082 vs. 0.160) and gradient variance by 2.18× compared to baselines.