Related papers: Predicting partially observable dynamical systems …

Probabilistic forecasting is crucial for real-world spatiotemporal systems, such as climate, energy, and urban environments, where quantifying uncertainty is essential for informed, risk-aware decision-making. While diffusion models have…

Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward…

Multiscale spatial structure complicates temporal prediction because small-scale spatial fluctuations influence large-scale evolution, yet resolving all scales is often intractable. Standard diffusion models do not address this problem…

Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…

Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…

Climate change is intensifying rainfall extremes, making high-resolution precipitation projections crucial for society to better prepare for impacts such as flooding. However, current Global Climate Models (GCMs) operate at spatial…

In this paper, we apply a recently developed nonparametric modeling approach, the "diffusion forecast", to predict the time-evolution of Fourier modes of turbulent dynamical systems. While the diffusion forecasting method assumes the…

The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…

The ability to predict the future trajectories of traffic participants is crucial for the safe and efficient operation of autonomous vehicles. In this paper, a diffusion-based generative model for multi-agent trajectory prediction is…

The problem of prediction of a given time series is examined on the basis of recent nonlinear dynamics theories. Particular attention is devoted to forecast the amplitude and phase of one of the most common solar indicator activity, the…

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

Missing values in multivariate time series data can harm machine learning performance and introduce bias. These gaps arise from sensor malfunctions, blackouts, and human error and are typically addressed by data imputation. Previous work…

This work presents an autoregressive generative diffusion model (DiffObs) to predict the global evolution of daily precipitation, trained on a satellite observational product, and assessed with domain-specific diagnostics. The model is…

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions,…

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges.…

Diffusion models, a family of generative models based on deep learning, have become increasingly prominent in cutting-edge machine learning research. With a distinguished performance in generating samples that resemble the observed data,…

Spreading processes play an increasingly important role in modeling for diffusion networks, information propagation, marketing and opinion setting. We address the problem of learning of a spreading model such that the predictions generated…

Data-driven weather prediction models exhibit promising performance and advance continuously. In particular, diffusion models represent fine-scale details without spatial smoothing, which is crucial for mesoscale predictions, such as heavy…