AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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arXiv preprint arXiv:2312.15796 , year=
26 Pith papers cite this work, alongside 62 external citations. Polarity classification is still indexing.
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GPROF-IR is a CNN-based retrieval that uses temporal context in geostationary IR observations to produce precipitation estimates with lower error than prior IR methods and climatological consistency with PMW retrievals for integration into IMERG V08.
PODiff performs conditional diffusion in a fixed, variance-ordered POD latent space to enable efficient probabilistic super-resolution of high-dimensional scientific fields with lower memory and better-calibrated uncertainty than pixel-space or dropout baselines.
A diffusion generative inverse model conditioned on temperature targets produces diverse, physically plausible urban vegetation patterns that achieve specified regional temperature shifts.
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
Augments the energy score objective for sample-based generative models with a differentiable decision loss that is itself a proper scoring rule, yielding targeted improvements on cost-sensitive regions in synthetic and real tasks.
SNAP-FM accelerates nonlinear constraint projection in Physics-Constrained Flow Matching by exploiting block-sparse Jacobian and KKT structures with ExaModels.jl, MadNLP.jl, and GPU sparse factorization on PDE benchmarks.
Patch-PODiff-ViT defines a structured latent space via patchwise POD for efficient diffusion-based super-resolution and direct analytic uncertainty quantification across scientific and natural images.
RMMD simultaneously distills diffusion models and optimizes rewards, yielding better FID-reward trade-offs on ImageNet than DI++, DRaFT and HyperNoise, and a 7.5x faster GenCast model that beats its teacher on 93% of weather variables while improving calibration.
Error-Conditioned Neural Solvers improve PDE prediction accuracy by using the residual field as network input for learned corrections, outperforming residual-minimization methods by up to 10x on turbulent flows and generalizing better under distribution shifts.
PhysMetrics.Weather is an evaluation framework that quantifies physical realism of ML weather prediction models using conservation, spectral, and dynamical metrics.
RealBench is a benchmark for data-driven weather forecasting that enforces operational conditions via a 2025 OOD test set, operational analysis, in-situ observations, and event-specific extreme metrics to expose gaps versus reanalysis-based evaluation.
DiffATS trains diffusion models directly on aligned Tucker tensor primitives that are proven to be homeomorphisms, delivering efficient unconditional and conditional generation across images, videos, and PDE data with high compression.
Diffusion model climate emulators provide probability density estimates that allow likelihood calculations and odds-ratio-based importance sampling for extreme events such as tropical cyclones.
DiffSRDA uses denoising diffusion models to perform uncertainty-aware spatiotemporal super-resolution data assimilation, achieving EnKF-like quality from low-resolution forecasts on an ocean jet testbed.
HealDA supplies ML-based initial conditions for AI weather models that produce forecasts trailing ERA5-initialized runs by less than one day of effective lead time, with the skill gap arising mainly from initial error size.
An offline-trained controller augments autoregressive diffusion models to perform fast, feed-forward data assimilation in chaotic spatiotemporal PDEs with order-of-magnitude speedups and improved accuracy over baselines.
Flow Marching jointly samples noise and physical time to learn a velocity field for generative PDE modeling, paired with a latent autoencoder and efficient transformer for large-scale pretraining on 2.5M trajectories.
DeepFleet develops and compares four foundation model architectures for multi-agent robot fleet coordination using warehouse data, finding robot-centric and graph-floor models most promising for prediction and scaling.
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
Diffusion models recover known ENSO variability structure from synthetic LIM data when given enough samples, but require pre-training on CMIP6 plus fine-tuning to match observations with the ~700 samples available in ERSSTv5.
Learned PDE solving should target transport over admissible futures via flow learners, not snapshot state regression.
A conditional diffusion model downscales global atmospheric forecasts from 100 km to 30 km resolution while improving probabilistic skill, matching power spectra, and preserving physical relationships.
A multimodal GNN ablation for Nordic precipitation nowcasting shows sparse point observations improve station and onset scores while NWP and CRPS losses improve radar-grid performance, indicating local and field skills are distinct targets.
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The physics of AI weather models
AI weather models may simulate the atmosphere via particle positions in latent space whose updates follow gradient flow on a learned free energy functional rather than conventional physical equations.
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GPROF-IR: An Improved Single-Channel Infrared Precipitation Retrieval for Merged Satellite Precipitation Products
GPROF-IR is a CNN-based retrieval that uses temporal context in geostationary IR observations to produce precipitation estimates with lower error than prior IR methods and climatological consistency with PMW retrievals for integration into IMERG V08.
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PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution
PODiff performs conditional diffusion in a fixed, variance-ordered POD latent space to enable efficient probabilistic super-resolution of high-dimensional scientific fields with lower memory and better-calibrated uncertainty than pixel-space or dropout baselines.
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Conflated Inverse Modeling to Generate Diverse and Temperature-Change Inducing Urban Vegetation Patterns
A diffusion generative inverse model conditioned on temperature targets produces diverse, physically plausible urban vegetation patterns that achieve specified regional temperature shifts.
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Latent Generative Solvers for Generalizable Long-Term Physics Simulation
LGS pretrained on 2.5M trajectories across 16 systems matches deterministic baselines at one step and halves 20-step error while using far less compute and adapting to held-out higher-resolution flows.
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Decision-Aware Training for Sample-Based Generative Models
Augments the energy score objective for sample-based generative models with a differentiable decision loss that is itself a proper scoring rule, yielding targeted improvements on cost-sensitive regions in synthetic and real tasks.
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SNAP-FM: Sparse Nonlinear Accelerated Projection for Physics-Constrained Generative Modeling
SNAP-FM accelerates nonlinear constraint projection in Physics-Constrained Flow Matching by exploiting block-sparse Jacobian and KKT structures with ExaModels.jl, MadNLP.jl, and GPU sparse factorization on PDE benchmarks.
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Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification
Patch-PODiff-ViT defines a structured latent space via patchwise POD for efficient diffusion-based super-resolution and direct analytic uncertainty quantification across scientific and natural images.
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Diffusion Fine-tuning with Rewarded Moment Matching Distillation
RMMD simultaneously distills diffusion models and optimizes rewards, yielding better FID-reward trade-offs on ImageNet than DI++, DRaFT and HyperNoise, and a 7.5x faster GenCast model that beats its teacher on 93% of weather variables while improving calibration.
-
Error-Conditioned Neural Solvers
Error-Conditioned Neural Solvers improve PDE prediction accuracy by using the residual field as network input for learned corrections, outperforming residual-minimization methods by up to 10x on turbulent flows and generalizing better under distribution shifts.
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PhysMetrics.Weather: An Evaluation Framework for Physical Consistency in ML Weather Models
PhysMetrics.Weather is an evaluation framework that quantifies physical realism of ML weather prediction models using conservation, spectral, and dynamical metrics.
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RealBench: Benchmarking Data-Driven Numerical Weather Forecasting Under Operational Conditions and Extreme Event Challenges
RealBench is a benchmark for data-driven weather forecasting that enforces operational conditions via a 2025 OOD test set, operational analysis, in-situ observations, and event-specific extreme metrics to expose gaps versus reanalysis-based evaluation.
-
DiffATS: Diffusion in Aligned Tensor Space
DiffATS trains diffusion models directly on aligned Tucker tensor primitives that are proven to be homeomorphisms, delivering efficient unconditional and conditional generation across images, videos, and PDE data with high compression.
-
Towards accurate extreme event likelihoods from diffusion model climate emulators
Diffusion model climate emulators provide probability density estimates that allow likelihood calculations and odds-ratio-based importance sampling for extreme events such as tropical cyclones.
-
Uncertainty-Aware Spatiotemporal Super-Resolution Data Assimilation with Diffusion Models
DiffSRDA uses denoising diffusion models to perform uncertainty-aware spatiotemporal super-resolution data assimilation, achieving EnKF-like quality from low-resolution forecasts on an ocean jet testbed.
-
HealDA: Highlighting the importance of initial errors in end-to-end AI weather forecasts
HealDA supplies ML-based initial conditions for AI weather models that produce forecasts trailing ERA5-initialized runs by less than one day of effective lead time, with the skill gap arising mainly from initial error size.
-
Control-Augmented Autoregressive Diffusion for Data Assimilation
An offline-trained controller augments autoregressive diffusion models to perform fast, feed-forward data assimilation in chaotic spatiotemporal PDEs with order-of-magnitude speedups and improved accuracy over baselines.
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Flow marching for a generative PDE foundation model
Flow Marching jointly samples noise and physical time to learn a velocity field for generative PDE modeling, paired with a latent autoencoder and efficient transformer for large-scale pretraining on 2.5M trajectories.
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DeepFleet: Multi-Agent Foundation Models for Mobile Robots
DeepFleet develops and compares four foundation model architectures for multi-agent robot fleet coordination using warehouse data, finding robot-centric and graph-floor models most promising for prediction and scaling.
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A Two-Phase Deep Learning Framework for Adaptive Time-Stepping in High-Speed Flow Modeling
ShockCast is a two-phase ML method that predicts adaptive timestep sizes to model high-speed flows with shocks more efficiently than fixed-step approaches.
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Learning Climate Variability from Scarce Data with Diffusion Models: A Test Case for ENSO
Diffusion models recover known ENSO variability structure from synthetic LIM data when given enough samples, but require pre-training on CMIP6 plus fine-tuning to match observations with the ~700 samples available in ERSSTv5.
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Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing
Learned PDE solving should target transport over admissible futures via flow learners, not snapshot state regression.
-
Downscaling weather forecasts from Low- to High-Resolution with Diffusion Models
A conditional diffusion model downscales global atmospheric forecasts from 100 km to 30 km resolution while improving probabilistic skill, matching power spectra, and preserving physical relationships.
-
Pointwise is Pointless? A Multimodal Ablation Study for Precipitation Nowcasting with Graph Neural Networks
A multimodal GNN ablation for Nordic precipitation nowcasting shows sparse point observations improve station and onset scores while NWP and CRPS losses improve radar-grid performance, indicating local and field skills are distinct targets.
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Towards a Foundation Model for the Martian Atmosphere
The paper reviews data sources, physical models, downstream applications, and AI techniques to outline considerations for building a foundation model for the Martian atmosphere.
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Extrapolation in Statistical Learning with Extreme Value Theory
A survey of recent methods that apply extreme value theory to enable extrapolation in statistical learning and machine learning.