Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be processed by autoregressive graph neural networks to recursively learn representations at each discrete point in time and space. Spatiotemporal graphs are often highly sparse, with time series characterized by multiple, concurrent, and long sequences of missing data, e.g., due to the unreliable underlying sensor network. In this context, autoregressive models can be brittle and exhibit unstable learning dynamics. The objective of this paper is, then, to tackle the problem of learning effective models to reconstruct, i.e., impute, missing data points by conditioning the reconstruction only on the available observations. In particular, we propose a novel class of attention-based architectures that, given a set of highly sparse discrete observations, learn a representation for points in time and space by exploiting a spatiotemporal propagation architecture aligned with the imputation task. Representations are trained end-to-end to reconstruct observations w.r.t. the corresponding sensor and its neighboring nodes. Compared to the state of the art, our model handles sparse data without propagating prediction errors or requiring a bidirectional model to encode forward and backward time dependencies. Empirical results on representative benchmarks show the effectiveness of the proposed method.

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD) provides a simple, data-driven approximation, but practical use is limited by sparse/noisy observations from continuous fields, reliance on linear approximations, and the lack of principled uncertainty quantification. To address these issues, we introduce Stochastic NODE-DMD, a probabilistic extension of DMD that models continuous-time, nonlinear dynamics while remaining interpretable. Our approach enables continuous spatiotemporal reconstruction at arbitrary coordinates and quantifies predictive uncertainty. Across four benchmarks, a synthetic setting and three physics-based flows, it surpasses a baseline in reconstruction accuracy when trained from only 10% observation density. It further recovers the dynamical structure by aligning learned modes and continuous-time eigenvalues with ground truth. Finally, on datasets with multiple realizations, our method learns a calibrated distribution over latent dynamics that preserves ensemble variability rather than averaging across regimes. Our code is available here.

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.

Data Assimilation (DA) plays a critical role in atmospheric science by reconstructing spatially continous estimates of the system state, which serves as initial conditions for scientific analysis. While recent advances in diffusion models have shown great potential for DA tasks, most existing approaches remain purely data-driven and often overlook the physical laws that govern complex atmospheric dynamics. As a result, they may yield physically inconsistent reconstructions that impair downstream applications. To overcome this limitation, we propose PhyDA, a physics-guided diffusion framework designed to ensure physical coherence in atmospheric data assimilation. PhyDA introduces two key components: (1) a Physically Regularized Diffusion Objective that integrates physical constraints into the training process by penalizing deviations from known physical laws expressed as partial differential equations, and (2) a Virtual Reconstruction Encoder that bridges observational sparsity for structured latent representations, further enhancing the model's ability to infer complete and physically coherent states. Experiments on the ERA5 reanalysis dataset demonstrate that PhyDA achieves superior accuracy and better physical plausibility compared to state-of-the-art baselines. Our results emphasize the importance of combining generative modeling with domain-specific physical knowledge and show that PhyDA offers a promising direction for improving real-world data assimilation systems.

Inferring full-body poses from Head Mounted Devices, which capture only 3-joint observations from the head and wrists, is a challenging task with wide AR/VR applications. Previous attempts focus on learning one-stage motion mapping and thus suffer from an over-large inference space for unobserved body joint motions. This often leads to unsatisfactory lower-body predictions and poor temporal consistency, resulting in unrealistic or incoherent motion sequences. To address this, we propose a powerful Multi-stage Avatar GEnerator named MAGE that factorizes this one-stage direct motion mapping learning with a progressive prediction strategy. Specifically, given initial 3-joint motions, MAGE gradually inferring multi-scale body part poses at different abstract granularity levels, starting from a 6-part body representation and gradually refining to 22 joints. With decreasing abstract levels step by step, MAGE introduces more motion context priors from former prediction stages and thus improves realistic motion completion with richer constraint conditions and less ambiguity. Extensive experiments on large-scale datasets verify that MAGE significantly outperforms state-of-the-art methods with better accuracy and continuity.

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be processed by autoregressive graph neural networks to recursively learn representations at each discrete point in time and space. Spatiotemporal graphs are often highly sparse, with time series characterized by multiple, concurrent, and long sequences of missing data, e.g., due to the unreliable underlying sensor network. In this context, autoregressive models can be brittle and exhibit unstable learning dynamics. The objective of this paper is, then, to tackle the problem of learning effective models to reconstruct, i.e., impute, missing data points by conditioning the reconstruction only on the available observations.

Data assimilation techniques are crucial for correcting the trajectory when modeling complex physical systems. A recently developed data assimilation method, Latent Ensemble Score Filter (Latent-EnSF), has shown great promise in addressing the key limitation of EnSF for highly sparse observations in high-dimensional and nonlinear data assimilation problems. It performs data assimilation in a latent space for encoded states and observations in every assimilation step, and requires costly full dynamics to be evolved in the original space. In this paper, we introduce Latent Dynamics EnSF (LD-EnSF), a novel methodology that completely avoids the full dynamics evolution and significantly accelerates the data assimilation process, which is especially valuable for complex dynamical problems that require fast data assimilation in real time. To accomplish this, we introduce a novel variant of Latent Dynamics Networks (LDNets) to effectively capture and preserve the system's dynamics within a very low-dimensional latent space. Additionally, we propose a new method for encoding sparse observations into the latent space using Long Short-Term Memory (LSTM) networks, which leverage not only the current step's observations, as in Latent-EnSF, but also all previous steps, thereby improving the accuracy and robustness of the observation encoding. We demonstrate the robustness, accuracy, and efficiency of the proposed method for two challenging dynamical systems with highly sparse (in both space and time) and noisy observations.

We investigate the use of the Senseiver, a transformer neural network designed for sparse sensing applications, to estimate full-field surface height measurements of tsunami waves from sparse observations. The model is trained on a large ensemble of simulated data generated via a shallow water equations solver, which we show to be a faithful reproduction for the underlying dynamics by comparison to historical events. We train the model on a dataset consisting of 8 tsunami simulations whose epicenters correspond to historical USGS earthquake records, and where the model inputs are restricted to measurements obtained at actively deployed buoy locations. We test the Senseiver on a dataset consisting of 8 simulations not included in training, demonstrating its capability for extrapolation. The results show remarkable resolution of fine scale phase and amplitude features from the true field, provided that at least a few of the sensors have obtained a non-zero signal. Throughout, we discuss which forecasting techniques can be improved by this method, and suggest ways in which the flexibility of the architecture can be leveraged to incorporate arbitrary remote sensing data (eg. HF Radar and satellite measurements) as well as investigate optimal sensor placements.