🧮 Scientific Computing

🧪 ICML2026 · 19 paper notes

📌 Same area in other venues: 📷 CVPR2026 (4) · 🔬 ICLR2026 (10) · 🤖 AAAI2026 (8) · 🧠 NeurIPS2025 (23) · 📹 ICCV2025 (1)

🔥 Top topics: Super-Resolution ×3 · Compression ×2 · Diffusion Models ×2 · Layout & Composition ×2 · Time-Series Forecasting ×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 instead of traditional first-order gradient flows. This enables the capture of richer collective phenomena such as periodicity and rotation, and allows interpolation and future prediction without requiring a reference process.

ANTIC: Adaptive Neural Temporal In-situ Compressor

To enable "on-the-fly" compression of PB-EB scale PDE simulation data, this work proposes ANTIC: a physics-aware temporal selector retains only physically important snapshots, and a neural field with LoRA continually fine-tunes to encode residuals between adjacent snapshots. Achieves 435× compression on 2D Kolmogorov flow and 6807× spatiotemporal compression on a 4.2 TiB 3D binary black hole merger simulation.

Discovering Ordinary Differential Equations with LLM-Based Qualitative and Quantitative Evaluation

DoLQ inserts a "Scientist Agent" into the search loop of LLM symbolic regression, performing both qualitative (physical plausibility) and quantitative (ablation MSE contribution) evaluations on candidates. This approach forces LLM-SR, which typically produces "low-error but bloated and physically nonsensical" equations, to converge to equations that are both numerically accurate and structurally compact.

Flow Sampling: Learning to Sample from Unnormalized Densities via Denoising Conditional Processes

This paper proposes Flow Sampling, which reverses flow matching/diffusion models from "data-driven" to "noise-driven"—constructing a denoising diffusion drift conditioned on source noise samples. On the interpolant, the detached model samples the energy gradient of \(X_1\) as the regression target, enabling the learning of efficient diffusion samplers in the absence of data, and naturally generalizing to constant curvature Riemannian manifolds.

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

Starting from four physical principles—locality, permutation equivariance, orientation covariance, and energy conservation/dissipation inequality—this work proves that any mesh-based physical dynamics satisfying these axioms can be locally reduced to a port-Hamiltonian form at the Jacobian level. In this form, the conserved interconnection structure \(J\) is entirely determined by the mesh topology (signed incidence matrix \(D_k\)), while the metric and dissipation are learned through \(G\) and \(R\). The proposed MeshFT-Net achieves near-zero energy drift, correct dispersion and momentum over long rollouts, and significantly outperforms MGN and HNN.

Meta-learning Structure-Preserving Dynamics

Systematically introduces modulation-based meta-learning (hyper-network maps latent code \(\bm{z}^{(k)}\) to hierarchical modulation parameters) into Hamiltonian / GENERIC neural networks, proposing two novel modulations—latent multi-rank (MR) and latent SVD-like modulation—enabling a shared network to few-shot adapt to a family of new parameter instances without knowing system parameters \(\bm{\mu}\), while strictly preserving energy conservation/dissipative structure.

MOOSE-Star: Unlocking Tractable Training for Scientific Discovery by Breaking the Complexity Barrier

MOOSE-Star decomposes the problem of "training an LLM to directly generate scientific hypotheses"—which originally requires searching a \(\mathcal{O}(N^k)\) combinatorial space—into two sequential subtasks: "inspiration retrieval + hypothesis composition." By further stacking hierarchical tree retrieval, bounded composition, and motivation planning, the optimal complexity is reduced from exponential to \(\mathcal{O}(\log N)\). The authors also release the TOMATO-Star dataset with 108,717 decomposition-annotated papers.

Phy-CoSF: Physics-Guided Continuous Spectral Fields Reconstruction and Super-Resolution for Snapshot Compressive Imaging

A train-render two-phase deep unfolding framework for snapshot compressive spectral imaging (CASSI), enabling arbitrary wavelength querying. Each unfolding stage incorporates a continuous spectral field (CoSF) prior module, consisting of a Fourier-Mamba-driven triple-branch cross-domain feature mixer, random frequency encoding, and a spectral synthesis head. Training on discrete wavelengths enables inference at any continuous wavelength, achieving continuous spectral reconstruction and zero-shot spectral super-resolution.

PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution

PODiff moves diffusion models from pixel space to a fixed, variance-ordered POD coefficient space, enabling a tiny MLP to achieve pixel-level diffusion accuracy on \(640\times 480\) SST downscaling tasks. Since reconstruction is linear, ensemble variance can be analytically mapped back to physical space via \(\Sigma_u=\Phi\Sigma_a\Phi^\top\), yielding spatially interpretable and well-calibrated uncertainty.

Rethink the Role of Neural Decoders in Quantum Error Correction

This work systematically re-implements five types of neural decoders—MLP, 3D-CNN, TCN, Transformer, and GNN—on surface codes with \(d\le9\), and incorporates "quantization + pruning + FPGA resource modeling" as first-class citizens in the training pipeline. The conclusion is: recent decoding performance is dominated by data volume rather than architectural complexity, and INT4 + QAT is a necessary prerequisite for achieving microsecond-level real-time decoding.

Saving Foundation Flow-Matching Priors for Inverse Problems

To address the phenomenon where foundation flow-matching models such as Stable Diffusion / Flux perform significantly worse than domain-specific or even untrained priors on inverse problems, the authors propose FMPlug: a method that uses a sample-guided, time-learnable warm-start combined with a sharp Gaussian shell constraint to force the latent variables of the foundation FM back onto the thin shell where it was actually "trained," thereby significantly restoring its effectiveness as a prior for inverse problems.

Semi-Supervised Neural Super-Resolution for Mesh-Based Simulations

SuperMeshNet employs two complementary MPNNs: the primary model predicts LR→HR, while the auxiliary model predicts the HR-HR difference corresponding to LR-LR. These models generate pseudo-labels for unpaired HR samples through mutual supervision. Combined with lightweight inductive biases at the node/message levels, this approach enables PDE mesh super-resolution to surpass fully supervised baselines using only 10% HR data, consistently reducing RMSE across six MPNN architectures.

Skipping the Zeros in Diffusion Models for Sparse Data Generation

SED transforms diffusion models from "full dense denoising across all dimensions" to "diffusion only on nonzero dimensions + autoregressive decoding of dimension-value pairs," reducing computation from linear in total dimensions to nearly constant in the number of nonzeros, while strictly preserving the semantic meaning of explicit zeros in scientific data.

Smoothness Errors in Dynamics Models and How to Avoid Them

The authors theoretically identify that Kiani et al.'s "unitary GNN" overly constrains physical systems like heat diffusion, which naturally smooth over time, due to its strict preservation of the Rayleigh quotient. They propose "relaxed unitary convolution" (R-UniGraph / R-UniMesh), extending the Rayleigh quotient-unitary convolution framework from graphs to triangular meshes, achieving superior performance over strong baselines on MeshPDE and WeatherBench22.

(Sparse) Attention to the Details: Preserving Spectral Fidelity in ML-based Weather Forecasting Models

MOSAIC addresses two types of spectral degradation in ML-based weather forecasting models—spectral damping from deterministic averaging and high-frequency aliasing from latent space compression—by combining probabilistic perturbation with mesh-aligned block-sparse attention on the HEALPix spherical mesh. With only 214M parameters at 1.5° resolution, it matches or surpasses models at 6× higher resolution, generating 24-member 10-day forecasts in 12 seconds on a single H100.

Teaching Molecular Dynamics to a Non-Autoregressive Ionic Transport Predictor

This work treats expensive atomic trajectories as a "privileged auxiliary modality" during training. A bimodal trainer first learns dynamics from trajectories, then distills its hidden representations via closed-form ridge regression into a non-autoregressive predictor that only sees equilibrium structures. On lithium ion mean squared displacement prediction, it is 200× faster and more accurate than autoregressive SOTA.

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 via Hodge orthogonal decomposition into a "low-frequency topological component (spectral basis) + high-frequency geometric component (FNO auxiliary grid)" dual-branch structure. A commutator correction term couples the two, enabling both high accuracy and conservation law fidelity on complex meshes.

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

This paper addresses the discretization bias in EM-BSDE training loss by proposing Un-EM-BSDE: single-step errors are averaged over two independent groups of Monte Carlo subsamples and then "multiplied" to form an unbiased estimator, eliminating bias without requiring Hessians. On benchmark PDEs such as HJB/BSB/AC, it matches the accuracy of Heun-BSDE / FS-PINNs but with only 1.79× the training time of EM-BSDE (compared to 42.91× for Heun-BSDE and 32.07× for FS-PINNs).

WeatherSyn: An Instruction Tuning MLLM For Weather Forecasting Report Generation

WeatherSyn decomposes the workflow of meteorological forecasters' report writing into a multimodal instruction task of "image interpretation → key point listing → report drafting." It first constructs the WSInstruct dataset, covering 31 US cities and 8 weather aspects, and then applies a three-stage SFT→RFT→DPO fine-tuning process on Qwen3-VL-8B. This enables an 8B open-source model to consistently outperform closed-source large models such as GPT-5-Nano and Claude-3.7-Sonnet across various evaluation metrics, while also demonstrating zero-shot generalization to unseen cities.