The work was conducted during the internship of Y uqi Chen and Y uchen Fang at Microsoft Research.

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no mechanism for adjusting the trajectory based on subsequent observations. Here, we demonstrate how this may be resolved through the well-understood mathematics of \emph{controlled differential equations}. The resulting \emph{neural controlled differential equation} model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations. We demonstrate that our model achieves state-of-the-art performance against similar (ODE or RNN based) models in empirical studies on a range of datasets. Finally we provide theoretical results demonstrating universal approximation, and that our model subsumes alternative ODE models.

The work was conducted during the internship of Y uqi Chen and Y uchen Fang at Microsoft Research.

Irregular sampling and high missingness are intrinsic challenges in modeling time series derived from electronic health records (EHRs), where clinical variables are measured at uneven intervals depending on workflow and intervention timing. To address this, we propose VITAL -- a variable-aware, large language model (LLM)-based framework tailored for learning from irregularly sampled physiological time series. VITAL differentiates between two distinct types of clinical variables: vital signs, which are frequently recorded and exhibit temporal patterns, and laboratory tests, which are measured sporadically and lack temporal structure. It reprograms vital signs into the language space, enabling the LLM to capture temporal context and reason over missing values through explicit encoding. In contrast, laboratory variables are embedded either using representative summary values or a learnable [Not measured] token, depending on their availability. Extensive evaluations on the benchmark datasets from the PhysioNet demonstrate that VITAL outperforms state-of-the-art methods designed for irregular time series. Furthermore, it maintains robust performance under high levels of missigness, which is prevalent in real-world clinical scenarios where key variables are often unavailable. Introduction Electronic Health Records (EHRs) digitally capture a wealth of patient data generated during routine clinical care. In particular, the Intensive Care Unit (ICU) is a data-rich environment due to the need for continuous, high-resolution patient monitoring. This has led to a surge of research in medical artificial intelligence (AI), with many studies leveraging publicly available EHR datasets in combination with machine learning techniques for tasks such as early warning, outcome prediction and patient stratification [1, 2, 3, 4, 5, 6, 7, 8, 9] A common approach in these studies is to model patient records as multivariate time series, capturing the temporal evolution of physiological and clinical variables. However, in practice, EHR time series are often irregularly sampled due to variations in clinical workflows, measurement protocols, and intervention timing.

We investigate the use of Long Short-Term Memory (LSTM) and Decomposition-LSTM (DLSTM) networks, combined with an ensemble algorithm, to predict solar flare occurrences using time-series data from the GOES catalog. The dataset spans from 2003 to 2023 and includes 151,071 flare events. Among approximately possible patterns, 7,552 yearly pattern windows are identified, highlighting the challenge of long-term forecasting due to the Sun's complex, self-organized criticality-driven behavior. A sliding window technique is employed to detect temporal quasi-patterns in both irregular and regularized flare time series. Regularization reduces complexity, enhances large flare activity, and captures active days more effectively. To address class imbalance, resampling methods are applied. LSTM and DLSTM models are trained on sequences of peak fluxes and waiting times from irregular time series, while LSTM and DLSTM, integrated with an ensemble approach, are applied to sliding windows of regularized time series with a 3-hour interval. Performance metrics, particularly TSS (0.74), recall (0.95) and the area under the curve (AUC=0.87) in the receiver operating characteristic (ROC), indicate that DLSTM with an ensemble approach on regularized time series outperforms other models, offering more accurate large-flare forecasts with fewer false errors compared to models trained on irregular time series. The superior performance of DLSTM is attributed to its ability to decompose time series into trend and seasonal components, effectively isolating random noise. This study underscores the potential of advanced machine learning techniques for solar flare prediction and highlights the importance of incorporating various solar cycle phases and resampling strategies to enhance forecasting reliability.

Forecasting irregular time series presents significant challenges due to two key issues: the vulnerability of models to mean regression, driven by the noisy and complex nature of the data, and the limitations of traditional error-based evaluation metrics, which fail to capture meaningful patterns and penalize unrealistic forecasts. These problems result in forecasts which are often misaligned with human intuition. To tackle these challenges, we propose an adversarial learning framework with a deep analysis of adversarial components. Specifically, we emphasize the importance of balancing the modeling of global distribution (overall patterns) and transition dynamics (localized temporal changes) to better capture the nuances of irregular time series. Overall, this research provides practical insights for improving models and evaluation metrics, and pioneers the application of adversarial learning in the domain of irregular time-series forecasting.

Developing a foundation model for time series forecasting across diverse domains has attracted significant attention in recent years. Existing works typically assume regularly sampled, well-structured data, limiting their applicability to more generalized scenarios where time series often contain missing values, unequal sequence lengths, and irregular time intervals between measurements. To cover diverse domains and handle variable regularities, we propose FlexTSF, a universal time series forecasting model that possesses better generalization and natively support both regular and irregular time series. FlexTSF produces forecasts in an autoregressive manner and incorporates three novel designs: VT-Norm, a normalization strategy to ablate data domain barriers, IVP Patcher, a patching module to learn representations from flexibly structured time series, and LED attention, an attention mechanism to seamlessly integrate these two and propagate forecasts with awareness of domain and time information. Experiments on 12 datasets show that FlexTSF outperforms state-of-the-art forecasting models respectively designed for regular and irregular time series. Furthermore, after self-supervised pre-training, FlexTSF shows exceptional performance in both zero-shot and few-show settings for time series forecasting. Time series forecasting, the task of predicting future values based on historical observations, plays an indispensable role across numerous domains, including finance, manufacturing, retail, healthcare, and meteorology (Lim & Zohren, 2021; De Gooijer & Hyndman, 2006).

Irregular time series, where data points are recorded at uneven intervals, are prevalent in healthcare settings, such as emergency wards where vital signs and laboratory results are captured at varying times. This variability, which reflects critical fluctuations in patient health, is essential for informed clinical decision-making. Existing self-supervised learning research on irregular time series often relies on generic pretext tasks like forecasting, which may not fully utilise the signal provided by irregular time series. There is a significant need for specialised pretext tasks designed for the characteristics of irregular time series to enhance model performance and robustness, especially in scenarios with limited data availability. This paper proposes a novel pretraining framework, EMIT, an event-based masking for irregular time series. EMIT focuses on masking-based reconstruction in the latent space, selecting masking points based on the rate of change in the data. This method preserves the natural variability and timing of measurements while enhancing the model's ability to process irregular intervals without losing essential information. Extensive experiments on the MIMIC-III and PhysioNet Challenge datasets demonstrate the superior performance of our event-based masking strategy. The code has been released at https://github.com/hrishi-ds/EMIT.

Neural ordinary differential equations are an attractive option for modelling temporal dynamics. However, a fundamental issue is that the solution to an ordinary differential equation is determined by its initial condition, and there is no mechanism for adjusting the trajectory based on subsequent observations. Here, we demonstrate how this may be resolved through the well-understood mathematics of \emph{controlled differential equations}. The resulting \emph{neural controlled differential equation} model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations. We demonstrate that our model achieves state-of-the-art performance against similar (ODE or RNN based) models in empirical studies on a range of datasets. Finally we provide theoretical results demonstrating universal approximation, and that our model subsumes alternative ODE models.