TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

PIER: Physics-Informed Environmental Retrieval for Time-Series Modeling

Accurate modeling of environmental systems is fundamental to scientific understanding and decision-making, yet remains challenging because observations are limited and physical dynamics vary across systems. Retrieval-augmented approaches offer a natural path to transfer knowledge across systems, but standard embedding-based retrieval does not guarantee consistency of underlying physical processes, since scenarios with similar embeddings may arise from different underlying mechanisms. We propose Physics-Informed Environmental Retrieval (PIER), a model-agnostic framework that augments embedding-based retrieval with a physics-aware stream that scores candidates by flux-response consistency with the target, using local verifiers trained on physics-derived flux features. A weight adjustment mechanism then learns per-scenario weights that adaptively balance the two retrieval streams based on diagnostic features summarizing physics-stream reliability. Experiments on 356 lakes across the Midwestern United States spanning 41 years show that PIER consistently outperforms baselines for water temperature and dissolved oxygen prediction, and serves as a general augmentation strategy across diverse backbones.

Physics-Preserving Latent Compression for Zero-Shot Resolution Transfer in 3D Turbulence

High-resolution turbulence modeling is essential for scientific computing, but remains constrained by the cost of direct numerical simulation and the scarcity of full-resolution data. Existing scientific compressors reduce storage but typically operate on per-frame representations, whereas learned compressors yield compact latents that are often resolution-dependent and weakly aligned with the physics of turbulence. This raises the need for a compression framework that reduces data size, preserves physical diagnostics, and transfers from low-resolution training fields to high-resolution test fields without retraining. In this paper, we propose Physics-Preserving Latent Compression (PPLC), a patch-local latent compressor for three-dimensional turbulence. Motivated by inertial-range scale similarity, PPLC treats fixed-size patches as transferable units and applies a shared variational autoencoder independently of the global grid size. It combines exact mean preservation, zero-mean fluctuation encoding, an invertible Haar wavelet front-end, shift-consistency regularization, and overlap-aware reconstruction. Instantiated on forced isotropic turbulence, PPLC is trained only on stride-downsampled 256^3 fields and transfers zero-shot to 1024^3 fields. Experiments show that PPLC improves the balance between reconstruction accuracy and physical fidelity over classical and learned baselines, keeping diagnostics such as dissipation, enstrophy, energy spectra, and incompressibility closer to the ground truth. Beyond turbulence compression, PPLC offers a general strategy for physics-preserving latent representations that support data-efficient scientific surrogate modeling.

LLM-as-a-Reviewer: Benchmarking Their Ability, Divergence, and Prompt Injection Resistance as Paper Reviewers

Large language models (LLMs) are increasingly used in academic peer review, yet their reliability, alignment with human judgment, and robustness to adversarial attacks remain poorly understood. We present a systematic benchmark of LLM-as-a-Reviewer on 898 papers stratified from NeurIPS and ICLR, evaluating 12 LLMs along three axes: rating calibration, divergence from human reviewers, and resistance to prompt injection embedded via an invisible font-mapping attack. We find that LLMs systematically overrate weaker submissions and diverge from humans in topical emphasis, under-flagging Clarity and over-flagging Reproducibility, while producing reviews two to three times longer with lower lexical diversity and a more standardized vocabulary. Prompt injection remains highly effective. Simple hidden instructions can promote low-scoring papers to acceptance-level ratings in a substantial fraction of cases, with effectiveness varying sharply across model families. While LLMs offer utility in structuring evaluations, their integration into peer review requires safeguards against both intrinsic biases and adversarial risks.

Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

Partial differential equations (PDEs) govern nearly every physical process in science and engineering, yet solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but learned PDE solvers have not undergone a comparable shift. Existing paradigms each capture part of the problem. Physics-informed neural networks embed residual structure, yet they are often difficult to optimize in stiff, multiscale, or large-domain regimes. Neural operators amortize across instances, yet they commonly inherit a snapshot-prediction view of solving and can degrade over long rollouts. Diffusion-based solvers model uncertainty, yet they are often built on a solver template that still centers on state regression. We argue that the core issue is the abstraction used to train learned solvers. Many models are asked to predict states, while many scientific settings require modeling how uncertainty moves through constrained dynamics. The relevant object is transport over physically admissible futures. This motivates \emph{flow learners}: models that parameterize transport vector fields and generate trajectories through integration, echoing the continuous dynamics that define PDE evolution. This physics-to-physics alignment supports continuous-time prediction, native uncertainty quantification, and new opportunities for physics-aware solver design. We explain why transport-based learning offers a stronger organizing principle for learned PDE solving and outline the research agenda that follows from this shift.

Role-Aware Conditional Inference for Spatiotemporal Ecosystem Carbon Flux Prediction

Accurate prediction of terrestrial ecosystem carbon fluxes (e.g., CO$_2$, GPP, and CH$_4$) is essential for understanding the global carbon cycle and managing its impacts. However, prediction remains challenging due to strong spatiotemporal heterogeneity: ecosystem flux responses are constrained by slowly varying regime conditions, while short-term fluctuations are driven by high-frequency dynamic forcings. Most existing learning-based approaches treat environmental covariates as a homogeneous input space, implicitly assuming a global response function, which leads to brittle generalization across heterogeneous ecosystems. In this work, we propose Role-Aware Conditional Inference (RACI), a process-informed learning framework that formulates ecosystem flux prediction as a conditional inference problem. RACI employs hierarchical temporal encoding to disentangle slow regime conditioners from fast dynamic drivers, and incorporates role-aware spatial retrieval that supplies functionally similar and geographically local context for each role. By explicitly modeling these distinct functional roles, RACI enables a model to adapt its predictions across diverse environmental regimes without training separate local models or relying on fixed spatial structures. We evaluate RACI across multiple ecosystem types (wetlands and agricultural systems), carbon fluxes (CO$_2$, GPP, CH$_4$), and data sources, including both process-based simulations and observational measurements. Across all settings, RACI consistently outperforms competitive spatiotemporal baselines, demonstrating improved accuracy and spatial generalization under pronounced environmental heterogeneity.

PEST: Physics-Enhanced Swin Transformer for 3D Turbulence Simulation

Accurate simulation of turbulent flows is fundamental to scientific and engineering applications. Direct numerical simulation (DNS) offers the highest fidelity but is computationally prohibitive, while existing data-driven alternatives struggle with stable long-horizon rollouts, physical consistency, and faithful simulation of small-scale structures. These challenges are particularly acute in three-dimensional (3D) settings, where the cubic growth of spatial degrees of freedom dramatically amplifies computational cost, memory demand, and the difficulty of capturing multi-scale interactions. To address these challenges, we propose a Physics-Enhanced Swin Transformer (PEST) for 3D turbulence simulation. PEST leverages a window-based self-attention mechanism to effectively model localized PDE interactions while maintaining computational efficiency. We introduce a frequency-domain adaptive loss that explicitly emphasizes small-scale structures, enabling more faithful simulation of high-frequency dynamics. To improve physical consistency, we incorporate Navier--Stokes residual constraints and divergence-free regularization directly into the learning objective. Extensive experiments on two representative turbulent flow configurations demonstrate that PEST achieves accurate, physically consistent, and stable autoregressive long-term simulations, outperforming existing data-driven baselines.

Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the emergence of various physics-aware data-driven approaches, the field still lacks a unified perspective to uncover their relationships, limitations, and appropriate roles in scientific workflows. To this end, we propose a unifying perspective to place two dominant paradigms: Physics-Informed Neural Networks (PINNs) and Neural Operators (NOs), within a shared design space. We organize existing methods from three fundamental dimensions: what is learned, how physical structures are integrated into the learning process, and how the computational load is amortized across problem instances. In this way, many challenges can be best understood as consequences of these structural properties of learning PDEs. By analyzing advances through this unifying view, our survey aims to facilitate the development of reliable learning-based PDE solvers and catalyze a synthesis of physics and data.

GREAT: Generalizable Representation Enhancement via Auxiliary Transformations for Zero-Shot Environmental Prediction

Environmental modeling faces critical challenges in predicting ecosystem dynamics across unmonitored regions due to limited and geographically imbalanced observation data. This challenge is compounded by spatial heterogeneity, causing models to learn spurious patterns that fit only local data. Unlike conventional domain generalization, environmental modeling must preserve invariant physical relationships and temporal coherence during augmentation. In this paper, we introduce Generalizable Representation Enhancement via Auxiliary Transformations (GREAT), a framework that effectively augments available datasets to improve predictions in completely unseen regions. GREAT guides the augmentation process to ensure that the original governing processes can be recovered from the augmented data, and the inclusion of the augmented data leads to improved model generalization. Specifically, GREAT learns transformation functions at multiple layers of neural networks to augment both raw environmental features and temporal influence. They are refined through a novel bi-level training process that constrains augmented data to preserve key patterns of the original source data. We demonstrate GREAT's effectiveness on stream temperature prediction across six ecologically diverse watersheds in the eastern U.S., each containing multiple stream segments. Experimental results show that GREAT significantly outperforms existing methods in zero-shot scenarios. This work provides a practical solution for environmental applications where comprehensive monitoring is infeasible.

Geo-Aware Models for Stream Temperature Prediction across Different Spatial Regions and Scales

Understanding environmental ecosystems is vital for the sustainable management of our planet. However,existing physics-based and data-driven models often fail to generalize to varying spatial regions and scales due to the inherent data heterogeneity presented in real environmental ecosystems. This generalization issue is further exacerbated by the limited observation samples available for model training. To address these issues, we propose Geo-STARS, a geo-aware spatio-temporal modeling framework for predicting stream water temperature across different watersheds and spatial scales. The major innovation of Geo-STARS is the introduction of geo-aware embedding, which leverages geographic information to explicitly capture shared principles and patterns across spatial regions and scales. We further integrate the geo-aware embedding into a gated spatio-temporal graph neural network. This design enables the model to learn complex spatial and temporal patterns guided by geographic and hydrological context, even with sparse or no observational data. We evaluate Geo-STARS's efficacy in predicting stream water temperature, which is a master factor for water quality. Using real-world datasets spanning 37 years across multiple watersheds along the eastern coast of the United States, Geo-STARS demonstrates its superior generalization performance across both regions and scales, outperforming state-of-the-art baselines. These results highlight the promise of Geo-STARS for scalable, data-efficient environmental monitoring and decision-making.