⚛️ Physics & Scientific Computing

🧪 ICML2026 · 33 paper notes

📌 Same area in other venues: 📷 CVPR2026 (2) · 🔬 ICLR2026 (69) · 🤖 AAAI2026 (15) · 🧠 NeurIPS2025 (57) · 📹 ICCV2025 (2) · 🧪 ICML2025 (20)

🔥 Top topics: Biomolecules ×2

A Call to Lagrangian Action: Learning Population Mechanics from Temporal Snapshots

Starting from the principle of least action, this paper proposes the Wasserstein Lagrangian Mechanics (WLM) framework to learn second-order population dynamics rather than traditional first-order gradient flow dynamics. This enables capturing richer collective phenomena such as periodicity and rotation, and allows for interpolation and future forecasting without requiring a reference process.

ANTIC: Adaptive Neural Temporal In-situ Compressor

To compress PB-EB scale PDE simulation data "on-the-fly," this paper proposes ANTIC: it utilizes a physics-aware temporal selector to retain only physically significant snapshots, and employs neural fields with LoRA continual fine-tuning to encode residuals between adjacent snapshots. It achieves \(435\times\) compression on 2D Kolmogorov flows and \(6807\times\) spatio-temporal joint compression on a 4.2 TiB 3D binary black hole merger simulation.

BALLAST: Bayesian Active Learning with Look-ahead Amendment for Sea-drifter Trajectories under Spatio-Temporal Vector Fields

The BALLAST algorithm is proposed to correct active learning utility estimates by sampling vector fields from the GP posterior and simulating future trajectories of Lagrangian observers. Additionally, the VaSE inference method is developed to increase GP posterior sampling efficiency by thousands of times, achieving approximately 16%-22% savings in deployment costs on synthetic and high-fidelity ocean flow fields.

Distribution Transformers: Fast Approximate Bayesian Inference With On-The-Fly Prior Adaptation

Distribution Transformer (DT) explicitly tokenizes the "prior distribution" into a set of Gaussian Mixture Model (GMM) components and injects "observations" into the decoder via cross-attention, learning an end-to-end mapping from "prior + data → posterior." While maintaining conjugacy within the same family (GMM→GMM) to support sequential filtering, it compresses inference time from minutes to milliseconds and allows arbitrary prior replacement at test time without retraining.

EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

EqGINO transforms GINO's GNO encoder, FNO backbone, and GNO decoder into SE(3) equivariant modules: GNO adopts relative distances as rotation-invariant kernels, and FNO utilizes "orbit-based weight sharing" to enforce isotropy (\(W(R\mathbf k)=W(\mathbf k)\)) in the frequency domain. This maintains the global receptive field of FNO while ensuring robustness to arbitrary rigid transformations in 3D PDE surrogates and reducing spectral weight complexity from \(\mathcal O(K^3)\) to \(\mathcal O(K)\).

Foundation Inference Models for Ordinary Differential Equations

FIM-ODE amortizes the process of "inferring ordinary differential equation vector fields from noisy trajectories" into pre-training. Using an 8M-parameter Transformer neural operator pre-trained solely on low-degree polynomial ODE priors, it performs zero-shot vector field prediction in a single forward pass. It matches or exceeds the symbolic regression baseline ODEFormer on ODEBench with approximately 1/10 the parameters and 1/80 the training data.

From Generalist to Specialist Representation

This paper provides the first fully nonparametric (no intervention, no functional constraints) proof for two-layer hierarchical identifiability: the temporal-task structure is identifiable via CI tests from a collider perspective, and task-relevant latents can be disentangled from generalist representations through sparsity regularization.

From Geometry to Dynamics: Learning Overdamped Langevin Dynamics from Sparse Observations with Geometric Constraints

To address the difficulty of accurately inferring stochastic dynamics when trajectories are sparsely sampled, this paper reformulates inference as a stochastic control problem. It utilizes the geometry of the system's invariant density (Riemannian metric + geodesics) to guide the reconstruction of unobserved paths, achieving significantly more accurate estimation of the drift function \(\mathbf{f}\) in extremely under-sampled overdamped Langevin systems compared to existing methods.

Generative Neural Operators Through Diffusion Last Layer

A "Diffusion Last Layer" (DLL) is appended to any neural operator backbone (FNO/DeepONet). An input-dependent basis \(\Phi_a\) is used to compress the target field into an \(r\)-dimensional coefficient vector, followed by a small MLP velocity field that performs conditional flow matching in the coefficient space. This upgrades deterministic operators into generative ones capable of sampling stochastic solutions and providing roll-out uncertainty.

Hermite-NGP: Gradient-Augmented Hash Encoding for Learning PDEs

The paper upgrades Instant-NGP's multi-resolution hash table to a "gradient-augmented" version—storing function values and all mixed partial derivatives at each hash grid point. It utilizes Hermite interpolation to reconstruct a \(C^1\) continuous, analytically twice-differentiable field, effectively enabling NGP for PINN-based PDE solving for the first time. It achieves up to a \(20\times\) error reduction over SOTA neural PDE solvers on 2D/3D benchmarks, with training times of only \(2\)–\(3.5\,\mathrm{ms}\) per epoch.

Interpretable Equivariant Marks for Contrastive Cosmological Inference

This paper replaces manually designed marking functions in cosmological "marked statistics" with an interpretable, equivariance-constrained neural mark. By using three local SO(3)-equivariant spherical harmonic filters to extract rotationally invariant morphological descriptors and aligning the marked two-point spectra with cosmological parameters via contrastive learning (InfoNCE + residualization), it tightens the marginal constraints of \(\sigma_8\) by \(2.9\times\) and \(\Omega_m\) by \(1.8\times\) on Quijote N-body simulations, successfully breaking the classical \(\Omega_m\)–\(\sigma_8\) degeneracy.

Iterative Refinement Neural Operators are Learned Fixed-Point Solvers: A Principled Approach to Spectral Bias Mitigation

The paper proposes an external weight-sharing U-Net refinement module \(\Phi_\theta\) for pre-trained neural operators (FNO/TFNO/WDSR, etc.). During inference, it iteratively updates the solution via \(h_{k+1}=h_k+\alpha\Phi_\theta(x,h_k)\), transforming a single forward pass into a "learned residual solver" that converges to a unique fixed point. This approach reduces errors by 34%–80% in tasks like turbulence, active matter, and ERA5 super-resolution, while maintaining stable extrapolation to twice the training iterations.

Learning to Refine: Spectral-Decoupled Iterative Refinement Framework for Precipitation Nowcasting

SDIR reformulates radar precipitation nowcasting (0–2 hours) as a "frequency-decoupled iterative refinement" process. It employs SFG-Former to extract stable low-frequency weather skeletons and FR-Refiner (utilizing Fourier Neural Operators) to progressively synthesize high-frequency convective details across frequency bands. A PCPSD loss, aligned with the Kolmogorov turbulence power law, replaces pure MSE to prevent over-smoothing. SDIR significantly outperforms both regression-based and diffusion-based SOTAs on CIKM, Shanghai, and SEVIR benchmarks.

Loss Landscape Diagnosis for Gradient-Based Gray-Scott System Inversion: Disentangling the Roles of PINN Components

The authors employ a minimalist approach—directly backpropagating steady-state losses through unrolled Gray-Scott simulations to invert PDE parameters without any surrogate models or neural networks—finding that optimization fails completely. By directly visualizing the loss landscape, they locate the pathology (plateaus and cliffs, with cliffs precisely aligned with bifurcation boundaries). Reinterpreting this minimalist probe as an ablation of PINNs, the study for the first time distinguishes the roles of PINN components: the residual loss independently smoothens the landscape (by implicitly encoding full PDE dynamics), while the neural network fails to fix the pathological parameter subspace and is only responsible for completing observed data.

\(\mathbb{R}^{2k}\) is Theoretically Large Enough for Embedding-based Top-\(k\) Retrieval

This paper proves that for three scoring functions—inner product, Euclidean distance, and cosine similarity—the Minimum Embeddable Dimension (MED) required to precisely retrieve all subsets of \(m\) objects with size \(\le k\) via score-thresholding is \(\Theta(k)\), independent of \(m\). With unit normalization and a positive score margin \(\epsilon\), the feasible margin for robust MED is locked by an upper bound \(\epsilon_\star(m,k)=m/\sqrt{k(m-1)(m-k)}\sim 1/\sqrt{k}\), while a Gaussian centroid construction provides a feasible upper bound of \(O(k^2\log m)\) dimensions.

Mesh Field Theory: Port–Hamiltonian Formulation of Mesh-Based Physics

Starting from four physical principles—"Locality + Permutation Equivariance + Orientation Covariance + Energy Conservation/Dissipation Inequality"—it is proven that any mesh physics dynamics satisfying these axioms can be locally reduced to a port-Hamiltonian form at the Jacobian level. In this formulation, the conservative interconnection structure \(J\) is fixed by the mesh topology (signed incidence matrix \(D_k\)), while metric and dissipation enter through learnable \(G\) and \(R\). The resulting MeshFT-Net achieves near-zero energy drift on long rollouts, preserves correct dispersion and momentum, and significantly outperforms MGN and HNN.

MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties

MōLe-Λ extends molecular orbital learning from predicting only Coupled-Cluster right-state \(T\) amplitudes to simultaneously predicting left-state \(\Lambda\) amplitudes. Using a single equivariant network to read out \((T_1, T_2, \Lambda_1, \Lambda_2)\) directly from localized Hartree–Fock orbitals, it achieves MAEs for energy and force of only 0.10 mHa and 0.12 mHa/Bohr on QM7. It derives response properties including dipole, quadrupole, polarizability, electron density, and pair density from the same learned "response state," accelerating calculations by over two orders of magnitude compared to CCSD+\(\Lambda\) solvers.

PINNfluence: Interpreting PINNs Through Influence Functions

This paper extends Influence Functions, a training data attribution method, to Physics-Informed Neural Networks (PINNs), proposing PINNfluence. By using linearized leave-one-out perturbation estimation, it attributes the prediction, loss, or physical quantities of a PINN simultaneously to each training point and each loss component. Based on this, it constructs a set of diagnostic metrics (loss component ratios, cancellation scores, temporal causality metrics, etc.) that consistently distinguish between "well-trained" and "poorly-trained" PINNs across five time-dependent PDEs, providing structural diagnostics that residual analysis fails to identify.

Quantum latent distributions in deep generative models

This study investigates when and why "latent space distributions generated by quantum processors" can enhance deep generative models. Theoretically, it proves that under specific network assumptions, quantum latent distributions enable generators to produce data distributions that classical latent distributions cannot efficiently approximate. Experimentally, using real and simulated photonic quantum processors, an apple-to-apple comparison is conducted on synthetic quantum datasets and the QM9 molecule dataset, revealing that statistics originating from quantum interference indeed lead to superior generative performance.

Quiver: Quantum-Informed Views for Enhanced Representations in Large ML Models

Quiver feeds categorical inputs into an additional Variational Quantum Circuit (VQC) to extract the Quantum Fisher Information Matrix (QFIM) as a "quantum geometric view." It then injects this into classical backbones using cross-attention (for Transformers) or residual gating (for GNNs), achieving consistent improvements across distinct physical tasks: JetClass top quark tagging and QM9 HOMO-LUMO gap regression.

Rethink the Role of Neural Decoders in Quantum Error Correction

This paper systematically re-evaluates five types of neural decoders (MLP, 3D-CNN, TCN, Transformer, and GNN) on surface codes with \(d\le9\). By integrating "quantization + pruning + FPGA resource modeling" as first-class citizens into the training pipeline, the study concludes that contemporary decoding performance is dominated by data volume rather than architectural complexity, and that INT4 + QAT is a necessary prerequisite for achieving microsecond-level real-time decoding.

REX: A Family of Reversible Exponential Stochastic Runge-Kutta Solvers

This paper proposes Rex—a family of algebraically reversible (stochastic) Runge-Kutta solvers constructed based on Lawson exponential integrators. It automatically transforms any explicit (S)RK scheme into a precisely invertible ODE/SDE solver, ensuring arbitrary high-order convergence and non-zero stability regions while achieving near machine-precision inversion for diffusion model image reconstruction/editing and Boltzmann sampling in flow models.

Score-Based Error Correcting Code Decoder

This paper proposes SB-ECC: reinterpreting the soft decoding of binary linear block codes as the reverse denoising of a Variance Exploding (VE) diffusion process. By using a time-unconditional score network that directly accepts signed channel observations \(\mathbf{y}\) to solve a parity-constraint-guided Probability Flow ODE, it achieves the best BER in 39 out of 42 code-SNR configurations, with an average SNR gain of 0.17 dB and a maximum of 0.46 dB.

Softplus Attention with Re-weighting Boosts Length Extrapolation in Large Language Models

The authors deconstruct traditional Softmax attention into two independent components: "non-negativity" and "L1 normalization." They demonstrate that L1 normalization, rather than the exponential function, is the critical factor. By replacing the exponential with Softplus paired with a dynamic length scale factor, they derive LSSA. Adding a power-function-based "re-weighting" for sharpening results in LSSAR, which maintains nearly constant validation loss at 16× training length and enables a GPT-109M to "rediscover" Newton's law of universal gravitation from trajectory data.

Spectrally Regularized Latent Flow Matching for Turbulence Generation

Replaces the common MSE-based compression VAE in latent flow matching for turbulence generation with a "partition-weighted log-spectral" objective. This specifically resolves the systematic underestimation of dissipation range magnitudes—improving spectral power retention from 25% to 94% during reconstruction and from 20% to 79% during unconditional generation, breaking the quality ceiling of MSE latent spaces with only 20 integration steps.

Speculative Sampling for Faster Molecular Dynamics

This paper transfers speculative sampling from language models to second-order Langevin molecular dynamics, proposing LSD: serial extrapolation using a fast draft potential and parallel verification using a slow target potential. By ensuring trajectory distributions strictly match the target model through reflection-maximal coupling, it achieves 3–9× lossless speedup on systems such as FCC copper.

Teaching Molecular Dynamics to a Non-Autoregressive Ionic Transport Predictor

This paper treats expensive atomic trajectories as "privileged auxiliary modalities" during training. A dual-modality trainer first learns dynamics from trajectories, which are then distilled into a non-autoregressive (NAR) predictor that only uses equilibrium structures via closed-form ridge regression. On lithium-ion mean squared displacement (MSD) prediction, the method is 200× faster and more accurate than autoregressive SOTA.

TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

To address the "time-entanglement" issue where standard spatio-temporal PINNs treat time as an extra input and share a single set of weights, TINNs formulate the network weights themselves as a function of time \(u_{\theta(t)}(\mathbf{x})\). This allows spatial representations to evolve over time. By utilizing a compact layer-wise time embedding to avoid parameter explosion and a Levenberg–Marquardt second-order optimizer, TINNs reduce relative \(L^2\) error by up to \(4\times\) and accelerate convergence by \(\approx 10\times\) across various time-dependent PDEs.

Topology-Preserving Neural Operator Learning via Hodge Decomposition

This paper proposes the Hodge Spectral Duality (HSD) neural operator, which decomposes the solution operator of manifold PDEs according to Hodge orthogonal decomposition into a dual-branch structure: a "low-frequency topological component (spectral basis) + high-frequency geometric component (FNO auxiliary grid)." These are coupled via a commutator correction term, achieving both high precision and conservation law fidelity on complex meshes.

TriForces: Augmenting Atomistic GNNs for Transferable Representations

TriForces decomposes atomistic graph neural networks into three parallel streams—"Composition-Structure-Interaction"—and overlays multi-objective self-supervised pre-training (LeJEPA + Denoising + Masking). This ensures that MLIPs are more robust in few-shot transfer, cross-domain fine-tuning, and similar structure retrieval compared to single-stream baselines.

Unbiased and Second-Order-Free Training for High-Dimensional PDEs

This paper addresses the discretization bias issue in EM-BSDE training loss by proposing Un-EM-BSDE: it forms an unbiased estimator by taking the "product" of single-step errors averaged over two independent Monte Carlo sub-samples. This approach eliminates bias without requiring the Hessian, achieving the accuracy of Heun-BSDE / FS-PINNs on benchmarks such as HJB, BSB, and AC, while training time remains only 1.79× that of EM-BSDE (compared to 42.91× for Heun-BSDE and 32.07× for FS-PINNs).

Understanding Catastrophic Forgetting In LoRA via Mean-Field Attention Dynamics

The authors formulate the Transformer self-attention as a mean-field particle system of interacting tokens and treat LoRA as a low-rank perturbation. They prove that forgetting is associated with two phase transition curves—"perturbation magnitude" and "network depth"—and provide a long-term stability condition controlled by the eigenvalue gap of \(V\).

Unveiling Multi-Regime Patterns in SciML: Diverse Failure Modes and Domain-Specific Optimization

Reveals three consistent failure modes in SciML models (PINNs, neural operators, etc.) through a systematic multi-domain diagnostic framework—and analyzes their loss landscape specificities to provide guidance for optimization method selection.