IMTS-Mixer: Mixer-Networks for Irregular Multivariate Time Series Forecasting

Forecasting Irregular Multivariate Time Series (IMTS) has recently emerged as a distinct research field, necessitating specialized models to address its unique challenges. While most forecasting literature assumes regularly spaced observations without missing values, many real-world datasets - particularly in healthcare, climate research, and biomechanics - violate these assumptions. Time Series (TS)-mixer models have achieved remarkable success in regular multivariate time series forecasting. However, they remain unexplored for IMTS due to their requirement for complete and evenly spaced observations. To bridge this gap, we introduce IMTS-Mixer, a novel forecasting architecture designed specifically for IMTS. Our approach retains the core principles of TS mixer models while introducing innovative methods to transform IMTS into fixed-size matrix representations, enabling their seamless integration with mixer modules. We evaluate IMTS-Mixer on a benchmark of four real-world datasets from various domains. Our results demonstrate that IMTS-Mixer establishes a new state-of-the-art in forecasting accuracy while also improving computational efficiency.

Physiome-ODE: A Benchmark for Irregularly Sampled Multivariate Time Series Forecasting Based on Biological ODEs

State-of-the-art methods for forecasting irregularly sampled time series with missing values predominantly rely on just four datasets and a few small toy examples for evaluation. While ordinary differential equations (ODE) are the prevalent models in science and engineering, a baseline model that forecasts a constant value outperforms ODE-based models from the last five years on three of these existing datasets. This unintuitive finding hampers further research on ODE-based models, a more plausible model family. In this paper, we develop a methodology to generate irregularly sampled multivariate time series (IMTS) datasets from ordinary differential equations and to select challenging instances via rejection sampling. Using this methodology, we create Physiome-ODE, a large and sophisticated benchmark of IMTS datasets consisting of 50 individual datasets, derived from real-world ordinary differential equations from research in biology. Physiome-ODE is the first benchmark for IMTS forecasting that we are aware of and an order of magnitude larger than the current evaluation setting of four datasets. Using our benchmark Physiome-ODE, we show qualitatively completely different results than those derived from the current four datasets: on Physiome-ODE ODE-based models can play to their strength and our benchmark can differentiate in a meaningful way between different IMTS forecasting models. This way, we expect to give a new impulse to research on ODE-based time series modeling.

Functional Latent Dynamics for Irregularly Sampled Time Series Forecasting

Irregularly sampled time series with missing values are often observed in multiple real-world applications such as healthcare, climate and astronomy. They pose a significant challenge to standard deep learn- ing models that operate only on fully observed and regularly sampled time series. In order to capture the continuous dynamics of the irreg- ular time series, many models rely on solving an Ordinary Differential Equation (ODE) in the hidden state. These ODE-based models tend to perform slow and require large memory due to sequential operations and a complex ODE solver. As an alternative to complex ODE-based mod- els, we propose a family of models called Functional Latent Dynamics (FLD). Instead of solving the ODE, we use simple curves which exist at all time points to specify the continuous latent state in the model. The coefficients of these curves are learned only from the observed values in the time series ignoring the missing values. Through extensive experi- ments, we demonstrate that FLD achieves better performance compared to the best ODE-based model while reducing the runtime and memory overhead. Specifically, FLD requires an order of magnitude less time to infer the forecasts compared to the best performing forecasting model.