Related papers: PDETime: Rethinking Long-Term Multivariate Time Se…

Transformer-based methods have achieved impressive results in time series forecasting. However, existing Transformers still exhibit limitations in sequence modeling as they tend to overemphasize temporal dependencies. This incurs additional…

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…

The equations of complex dynamical systems may not be identified by expert knowledge, especially if the underlying mechanisms are unknown. Data-driven discovery methods address this challenge by inferring governing equations from…

Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in…

We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…

High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated for modeling a given…

In the real world, long sequence time-series forecasting (LSTF) is needed in many cases, such as power consumption prediction and air quality prediction.Multi-dimensional long time series model has more strict requirements on the model,…

Pre-trained Large Language Models (LLMs) encapsulate large amounts of knowledge and take enormous amounts of compute to train. We make use of this resource, together with the observation that LLMs are able to transfer knowledge and…

Time series analysis is crucial for understanding dynamics of complex systems. Recent advances in foundation models have led to task-agnostic Time Series Foundation Models (TSFMs) and Large Language Model-based Time Series Models (TSLLMs),…

Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed…

Neural surrogates for partial differential equations (PDEs) have become popular due to their potential to quickly simulate physics. With a few exceptions, neural surrogates generally treat the forward evolution of time-dependent PDEs as a…

Large language models (LLMs) have been introduced to time series forecasting (TSF) to incorporate contextual knowledge beyond numerical signals. However, existing studies question whether LLMs provide genuine benefits, often reporting…

Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE…

Time series prediction with neural networks has been the focus of much research in the past few decades. Given the recent deep learning revolution, there has been much attention in using deep learning models for time series prediction, and…

Sequential modelling of high-dimensional data is an important problem that appears in many domains including model-based reinforcement learning and dynamics identification for control. Latent variable models applied to sequential data…

Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…

Time series sequence prediction and modelling has proven to be a challenging endeavor in real world datasets. Two key issues are the multi-dimensionality of data and the interaction of independent dimensions forming a latent output signal,…

We propose the Identifiable Variational Dynamic Factor Model (iVDFM), which learns latent factors from multivariate time series with identifiability guarantees. By applying iVAE-style conditioning to the innovation process driving the…

Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer…