Strictly Constrained Generative Modeling via Split Augmented Langevin Sampling

Deep generative models hold great promise for representing complex physical systems, but their deployment is currently limited by the lack of guarantees on the physical plausibility of the generated outputs. Ensuring that known physical constraints are enforced is therefore critical when applying generative models to scientific and engineering problems. We address this limitation by developing a principled framework for sampling from a target distribution while rigorously satisfying physical constraints. Leveraging the variational formulation of Langevin dynamics, we propose Split Augmented Langevin (SAL), a novel primal-dual sampling algorithm that enforces constraints progressively through variable splitting, with convergence guarantees. While the method is developed theoretically for Langevin dynamics, we demonstrate its effective applicability to diffusion models. In particular, we use constrained diffusion models to generate physical fields satisfying energy and mass conservation laws. We apply our method to diffusion-based data assimilation on a complex physical system, where enforcing physical constraints substantially improves both forecast accuracy and the preservation of critical conserved quantities. We also demonstrate the potential of SAL for challenging feasibility problems in optimal control.

Deep Generative Data Assimilation in Multimodal Setting

Robust integration of physical knowledge and data is key to improve computational simulations, such as Earth system models. Data assimilation is crucial for achieving this goal because it provides a systematic framework to calibrate model outputs with observations, which can include remote sensing imagery and ground station measurements, with uncertainty quantification. Conventional methods, including Kalman filters and variational approaches, inherently rely on simplifying linear and Gaussian assumptions, and can be computationally expensive. Nevertheless, with the rapid adoption of data-driven methods in many areas of computational sciences, we see the potential of emulating traditional data assimilation with deep learning, especially generative models. In particular, the diffusion-based probabilistic framework has large overlaps with data assimilation principles: both allows for conditional generation of samples with a Bayesian inverse framework. These models have shown remarkable success in text-conditioned image generation or image-controlled video synthesis. Likewise, one can frame data assimilation as observation-conditioned state calibration. In this work, we propose SLAMS: Score-based Latent Assimilation in Multimodal Setting. Specifically, we assimilate in-situ weather station data and ex-situ satellite imagery to calibrate the vertical temperature profiles, globally. Through extensive ablation, we demonstrate that SLAMS is robust even in low-resolution, noisy, and sparse data settings. To our knowledge, our work is the first to apply deep generative framework for multimodal data assimilation using real-world datasets; an important step for building robust computational simulators, including the next-generation Earth system models. Our code is available at: https://github.com/yongquan-qu/SLAMS

Joint Parameter and Parameterization Inference with Uncertainty Quantification through Differentiable Programming

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations that govern many problems ranging from weather and climate prediction to turbulence simulations. Recent advances have seen machine learning (ML) increasingly applied to model these subgrid processes, resulting in the development of hybrid physics-ML models through the integration with numerical solvers. In this work, we introduce a novel framework for the joint estimation and uncertainty quantification of physical parameters and machine learning parameterizations in tandem, leveraging differentiable programming. Achieved through online training and efficient Bayesian inference within a high-dimensional parameter space, this approach is enabled by the capabilities of differentiable programming. This proof of concept underscores the substantial potential of differentiable programming in synergistically combining machine learning with differential equations, thereby enhancing the capabilities of hybrid physics-ML modeling.

ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction

Accurate prediction of climate in the subseasonal-to-seasonal scale is crucial for disaster readiness, reduced economic risk, and improved policy-making amidst climate change. Yet, S2S prediction remains challenging due to the chaotic nature of the system. At present, existing benchmarks for weather and climate applications, tend to (1) have shorter forecasting range of up-to 14 days, (2) do not include a wide range of operational baseline forecasts, and (3) lack physics-based constraints for explainability. Thus, we propose ChaosBench, a large-scale, multi-channel, physics-based benchmark for S2S prediction. ChaosBench has over 460K frames of real-world observations and simulations, each with 60 variable-channels and spanning for up-to 45 years. We also propose several physics-based, in addition to vision-based metrics, that enables for a more physically-consistent model. Furthermore, we include a diverse set of physics-based forecasts from 4 national weather agencies as baselines to our data-driven counterpart. We establish two tasks that vary in complexity: full and sparse dynamics prediction. Our benchmark is one of the first to perform large-scale evaluation on existing models including PanguWeather, FourCastNetV2, GraphCast, and ClimaX, and finds methods originally developed for weather-scale applications fails on S2S task. We release our benchmark code and datasets at https://leap-stc.github.io/ChaosBench.