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Machine learning models play a vital role in time series forecasting. These models, however, often overlook an important element: point uncertainty estimates. Incorporating these estimates is crucial for effective risk management, informed…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

We introduce MoTIF, a mode-structured tensor framework for multi-parametric approximation, super-resolution, and temporal forecasting of high-dimensional unsteady systems. The methodology leverages High-Order Singular Value Decomposition…

Inferring relations from correlational data allows researchers across the sciences to uncover complex connections between variables for insights into the underlying mechanisms. The researchers often represent inferred relations using…

The recent revolution in data-driven methods for weather forecasting has lead to a fragmented landscape of complex, bespoke architectures and training strategies, obscuring the fundamental drivers of forecast accuracy. Here, we demonstrate…

While diffusion models have achieved great success in generating continuous signals such as images and audio, it remains elusive for diffusion models in learning discrete sequence data like natural languages. Although recent advances…

Image noise modeling is a long-standing problem with many applications in computer vision. Early attempts that propose simple models, such as signal-independent additive white Gaussian noise or the heteroscedastic Gaussian noise model…

Long-term time series forecasting is essential in areas like finance and weather prediction. Besides traditional methods that operate in the time domain, many recent models transform time series data into the frequency domain to better…

We consider the problem of designing almost optimal predictors for dynamical systems from a finite sequence of noisy observations and incomplete knowledge of the dynamics and the noise. We first discuss the properties of the optimal (Bayes)…

As parallel codes are scaled to larger computing systems, performance models play a crucial role in identifying potential bottlenecks. However, constructing these models analytically is often challenging. Empirical models based on…

Making accurate forecasts for a complex system is a challenge in various practical applications. The major difficulty in solving such a problem concerns nonlinear spatiotemporal dynamics with time-varying characteristics. Takens' delay…

Accurate spatiotemporal pattern analysis is critical in fields such as urban traffic, meteorology, and public health monitoring. However, existing methods face performance bottlenecks, typically yielding only incremental gains and often…

Multivariate time series forecasting is essential in domains such as finance, transportation, climate, and energy. However, existing patch-based methods typically adopt fixed-length segmentation, overlooking the heterogeneity of local…

Sensitivity of deep-neural models to input noise is known to be a challenging problem. In NLP, model performance often deteriorates with naturally occurring noise, such as spelling errors. To mitigate this issue, models may leverage…

Denoising diffusion probabilistic models are able to generate synthetic sensor signals. The training process of such a model is controlled by a loss function which measures the difference between the noise that was added in the forward…

Compressed Neural Networks have the potential to enable deep learning across new applications and smaller computational environments. However, understanding the range of learning tasks in which such models can succeed is not well studied.…

Diffusion models have become fundamental tools for modeling data distributions in machine learning. Despite their success, these models face challenges when generating data with extreme brightness values, as evidenced by limitations…

Time series forecasting is important in many fields that require accurate predictions for decision-making. Patching techniques, commonly used and effective in time series modeling, help capture temporal dependencies by dividing the data…

Delay-coordinate embedding is a powerful, time-tested mathematical framework for reconstructing the dynamics of a system from a series of scalar observations. Most of the associated theory and heuristics are overly stringent for real-world…

Efficiently modeling spatio-temporal (ST) physical processes and observations presents a challenging problem for the deep learning community. Many recent studies have concentrated on meticulously reconciling various advantages, leading to…