Related papers: Prediction in Projection: A new paradigm in delay-…

Recent time-series foundation models exhibit strong abilities to predict physical systems. These abilities include zero-shot forecasting, in which a model forecasts future states of a system given only a short trajectory as context, without…

The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…

The celebrated Mackey-Glass model describes the dynamics of physiological \textit{delayed} systems in which the actual evolution depends on the values of the variables at some \textit{previous} times. This kind of systems are usually…

Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

We empirically demonstrate that a transformer pre-trained on country-scale unlabeled human mobility data learns embeddings capable, through fine-tuning, of developing a deep understanding of the target geography and its corresponding…

Deep learning models have gained great success in many real-world applications. However, most existing networks are typically designed in heuristic manners, thus lack of rigorous mathematical principles and derivations. Several recent…

We propose a dynamic programming algorithm that constructs delay-optimized circuits for alternating And-Or paths with prescribed input arrival times. Our algorithm fulfills best-known approximation guarantees and empirically outperforms…

Delays endanger safety of autonomous systems operating in a rapidly changing environment, such as nondeterministic surrounding traffic participants in autonomous driving and high-speed racing. Unfortunately, delays are typically not…

Optimal decision-making compels us to anticipate the future at different horizons. However, in many domains connecting together predictions from multiple time horizons and abstractions levels across their organization becomes all the more…

Driven by the explosion of data and the impact of real-world networks, a wide array of mathematical models have been proposed to understand the structure and evolution of such systems, especially in the temporal context. Recent advances in…

Time delays increase the effective dimensionality of reservoirs, thus suggesting that time delays in reservoirs can enhance their performance, particularly their memory and prediction abilities. We find new closed-form expressions for…

Time-series forecasting remains difficult in real-world settings because temporal patterns operate at multiple scales, from broad contextual trends to fast, fine-grained fluctuations that drive critical decisions. Existing neural models…

A novel framework for hierarchical forecast updating is presented, addressing a critical gap in the forecasting literature. By assuming a temporal hierarchy structure, the innovative approach extends hierarchical forecast reconciliation to…

Producing probabilistic forecasts for large collections of similar and/or dependent time series is a practically relevant and challenging task. Classical time series models fail to capture complex patterns in the data, and multivariate…

Exploring the bridge between historical and future motion behaviors remains a central challenge in human motion prediction. While most existing methods incorporate a reconstruction task as an auxiliary task into the decoder, thereby…

Predicting human motion in unstructured and dynamic environments is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose to encode…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…