Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting

Weather forecasting is essential but remains computationally intensive and physically incomplete in traditional numerical weather prediction (NWP) methods. Deep learning (DL) models offer efficiency and accuracy but often ignore physical laws, limiting interpretability and generalization. We propose PhyDL-NWP, a physics-guided deep learning framework that integrates physical equations with latent force parameterization into data-driven models. It predicts weather variables from arbitrary spatiotemporal coordinates, computes physical terms via automatic differentiation, and uses a physics-informed loss to align predictions with governing dynamics. PhyDL-NWP enables resolution-free downscaling by modeling weather as a continuous function and fine-tunes pre-trained models with minimal overhead, achieving up to 170x faster inference with only 55K parameters. Experiments show that PhyDL-NWP improves both forecasting performance and physical consistency.

R&D-Agent: Automating Data-Driven AI Solution Building Through LLM-Powered Automated Research, Development, and Evolution

Recent advances in AI and ML have transformed data science, yet increasing complexity and expertise requirements continue to hinder progress. While crowdsourcing platforms alleviate some challenges, high-level data science tasks remain labor-intensive and iterative. To overcome these limitations, we introduce R&D-Agent, a dual-agent framework for iterative exploration. The Researcher agent uses performance feedback to generate ideas, while the Developer agent refines code based on error feedback. By enabling multiple parallel exploration traces that merge and enhance one another, R&D-Agent narrows the gap between automated solutions and expert-level performance. Evaluated on MLE-Bench, R&D-Agent emerges as the top-performing machine learning engineering agent, demonstrating its potential to accelerate innovation and improve precision across diverse data science applications. We have open-sourced R&D-Agent on GitHub: https://github.com/microsoft/RD-Agent.

Generating Full-field Evolution of Physical Dynamics from Irregular Sparse Observations

Modeling and reconstructing multidimensional physical dynamics from sparse and off-grid observations presents a fundamental challenge in scientific research. Recently, diffusion-based generative modeling shows promising potential for physical simulation. However, current approaches typically operate on on-grid data with preset spatiotemporal resolution, but struggle with the sparsely observed and continuous nature of real-world physical dynamics. To fill the gaps, we present SDIFT, Sequential DIffusion in Functional Tucker space, a novel framework that generates full-field evolution of physical dynamics from irregular sparse observations. SDIFT leverages the functional Tucker model as the latent space representer with proven universal approximation property, and represents observations as latent functions and Tucker core sequences. We then construct a sequential diffusion model with temporally augmented UNet in the functional Tucker space, denoising noise drawn from a Gaussian process to generate the sequence of core tensors. At the posterior sampling stage, we propose a Message-Passing Posterior Sampling mechanism, enabling conditional generation of the entire sequence guided by observations at limited time steps. We validate SDIFT on three physical systems spanning astronomical (supernova explosions, light-year scale), environmental (ocean sound speed fields, kilometer scale), and molecular (organic liquid, millimeter scale) domains, demonstrating significant improvements in both reconstruction accuracy and computational efficiency compared to state-of-the-art approaches.

Generalized Temporal Tensor Decomposition with Rank-revealing Latent-ODE

Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by incorporating continuous timestamps in latent factors, they still struggle with general tensor data with continuous indexes not only in the temporal mode but also in other modes, such as spatial coordinates in climate data. Additionally, the problem of determining the tensor rank remains largely unexplored in temporal tensor models. To address these limitations, we propose \underline{G}eneralized temporal tensor decomposition with \underline{R}ank-r\underline{E}vealing laten\underline{T}-ODE (GRET). Our approach encodes continuous spatial indexes as learnable Fourier features and employs neural ODEs in latent space to learn the temporal trajectories of factors. To automatically reveal the rank of temporal tensors, we introduce a rank-revealing Gaussian-Gamma prior over the factor trajectories. We develop an efficient variational inference scheme with an analytical evidence lower bound, enabling sampling-free optimization. Through extensive experiments on both synthetic and real-world datasets, we demonstrate that GRET not only reveals the underlying ranks of temporal tensors but also significantly outperforms existing methods in prediction performance and robustness against noise.

Diffusion-Generative Multi-Fidelity Learning for Physical Simulation

Multi-fidelity surrogate learning is important for physical simulation related applications in that it avoids running numerical solvers from scratch, which is known to be costly, and it uses multi-fidelity examples for training and greatly reduces the cost of data collection. Despite the variety of existing methods, they all build a model to map the input parameters outright to the solution output. Inspired by the recent breakthrough in generative models, we take an alternative view and consider the solution output as generated from random noises. We develop a diffusion-generative multi-fidelity (DGMF) learning method based on stochastic differential equations (SDE), where the generation is a continuous denoising process. We propose a conditional score model to control the solution generation by the input parameters and the fidelity. By conditioning on additional inputs (temporal or spacial variables), our model can efficiently learn and predict multi-dimensional solution arrays. Our method naturally unifies discrete and continuous fidelity modeling. The advantage of our method in several typical applications shows a promising new direction for multi-fidelity learning.

Functional Bayesian Tucker Decomposition for Continuous-indexed Tensor Data

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors). A fundamental assumption of such decomposition is that there were finite objects in each aspect or mode, corresponding to discrete indexes of data entries. However, many real-world data are not naturally posed in the setting. For example, geographic data is represented as continuous indexes of latitude and longitude coordinates, and cannot fit tensor models directly. To generalize Tucker decomposition to such scenarios, we propose Functional Bayesian Tucker Decomposition (FunBaT). We treat the continuous-indexed data as the interaction between the Tucker core and a group of latent functions. We use Gaussian processes (GP) as functional priors to model the latent functions, and then convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE) to reduce computational cost. An efficient inference algorithm is further developed for scalable posterior approximation based on advanced message-passing techniques. The advantage of our method is shown in both synthetic data and several real-world applications.

Solving High Frequency and Multi-Scale PDEs with Gaussian Processes

Machine learning based solvers have garnered much attention in physical simulation and scientific computing, with a prominent example, physics-informed neural networks (PINNs). However, PINNs often struggle to solve high-frequency and multi-scale PDEs, which can be due to spectral bias during neural network training. To address this problem, we resort to the Gaussian process (GP) framework. To flexibly capture the dominant frequencies, we model the power spectrum of the PDE solution with a student t mixture or Gaussian mixture. We then apply the inverse Fourier transform to obtain the covariance function (according to the Wiener-Khinchin theorem). The covariance derived from the Gaussian mixture spectrum corresponds to the known spectral mixture kernel. We are the first to discover its rationale and effectiveness for PDE solving. Next,we estimate the mixture weights in the log domain, which we show is equivalent to placing a Jeffreys prior. It automatically induces sparsity, prunes excessive frequencies, and adjusts the remaining toward the ground truth. Third, to enable efficient and scalable computation on massive collocation points, which are critical to capture high frequencies, we place the collocation points on a grid, and multiply our covariance function at each input dimension. We use the GP conditional mean to predict the solution and its derivatives so as to fit the boundary condition and the equation itself. As a result, we can derive a Kronecker product structure in the covariance matrix. We use Kronecker product properties and multilinear algebra to greatly promote computational efficiency and scalability, without any low-rank approximations. We show the advantage of our method in systematic experiments.

Streaming Factor Trajectory Learning for Temporal Tensor Decomposition

Practical tensor data is often along with time information. Most existing temporal decomposition approaches estimate a set of fixed factors for the objects in each tensor mode, and hence cannot capture the temporal evolution of the objects' representation. More important, we lack an effective approach to capture such evolution from streaming data, which is common in real-world applications. To address these issues, we propose Streaming Factor Trajectory Learning for temporal tensor decomposition. We use Gaussian processes (GPs) to model the trajectory of factors so as to flexibly estimate their temporal evolution. To address the computational challenges in handling streaming data, we convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE). We develop an efficient online filtering algorithm to estimate a decoupled running posterior of the involved factor states upon receiving new data. The decoupled estimation enables us to conduct standard Rauch-Tung-Striebel smoothing to compute the full posterior of all the trajectories in parallel, without the need for revisiting any previous data. We have shown the advantage of SFTL in both synthetic tasks and real-world applications. The code is available at {https://github.com/xuangu-fang/Streaming-Factor-Trajectory-Learning}.

Dynamic Tensor Decomposition via Neural Diffusion-Reaction Processes

Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the structural knowledge within the sparsely observed tensor entries. To overcome these limitations and to better capture the underlying temporal structure, we propose Dynamic EMbedIngs fOr dynamic Tensor dEcomposition (DEMOTE). We develop a neural diffusion-reaction process to estimate dynamic embeddings for the entities in each tensor mode. Specifically, based on the observed tensor entries, we build a multi-partite graph to encode the correlation between the entities. We construct a graph diffusion process to co-evolve the embedding trajectories of the correlated entities and use a neural network to construct a reaction process for each individual entity. In this way, our model can capture both the commonalities and personalities during the evolution of the embeddings for different entities. We then use a neural network to model the entry value as a nonlinear function of the embedding trajectories. For model estimation, we combine ODE solvers to develop a stochastic mini-batch learning algorithm. We propose a stratified sampling method to balance the cost of processing each mini-batch so as to improve the overall efficiency. We show the advantage of our approach in both simulation study and real-world applications. The code is available at https://github.com/wzhut/Dynamic-Tensor-Decomposition-via-Neural-Diffusion-Reaction-Processes.

BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition

In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local horizon, which means models are trained by splitting the long sequence into batches of fit-sized patches. This local horizon can make models ignore global trends or periodic patterns. More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications. Thirdly, most existing methods are learned in an offline manner. Thus, it is not suitable for many applications with fast-arriving streaming data. To overcome these limitations, we propose \ours: Bayesian Online Multivariate Time series Imputation with functional decomposition. We treat the multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We apply a group of Gaussian Processes (GPs) with different kernels as functional priors to fit the factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary time stamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets.