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This study introduces Universal Delay Embedding (UDE), a pretrained foundation model designed to revolutionize time-series forecasting through principled integration of delay embedding representation and Koopman operator prediction.…

Missing data frequently arises across diverse domains, including time-series and image domains. In the real world, missing occurrences often depend on the unobservable values themselves, which are referred to as Missing Not at Random…

Ordinary differential equations (ODEs), via their induced flow maps, provide a powerful framework to parameterize invertible transformations for the purpose of representing complex probability distributions. While such models have achieved…

We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…

Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…

High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in…

We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…

Missing data is a major challenge in clinical research. In electronic medical records, often a large fraction of the values in laboratory tests and vital signs are missing. The missingness can lead to biased estimates and limit our ability…

To comply with AI and data regulations, the need to forget private or copyrighted information from trained machine learning models is increasingly important. The key challenge in unlearning is forgetting the necessary data in a timely…

With the recent renaissance of deep convolution neural networks, encouraging breakthroughs have been achieved on the supervised recognition tasks, where each class has sufficient training data and fully annotated training data. However, to…

Recent machine learning advances have proposed black-box estimation of unknown continuous-time system dynamics directly from data. However, earlier works are based on approximative ODE solutions or point estimates. We propose a novel…

In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises:…

Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…

Several applications of Internet of Things (IoT) technology involve capturing data from multiple sensors resulting in multi-sensor time series. Existing neural networks based approaches for such multi-sensor or multivariate time series…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

This work is focussed on the inversion task of inferring the distribution over parameters of interest leading to multiple sets of observations. The potential to solve such distributional inversion problems is driven by increasing…

Dynamic astrophysical phenomena are predominantly described by differential equations, yet our understanding of these systems is constrained by our incomplete grasp of non-linear physics and scarcity of comprehensive datasets. As such,…

Simulation-based inference (SBI) methods typically require fully observed data to infer parameters of models with intractable likelihood functions. However, datasets often contain missing values due to incomplete observations, data…

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

The ability to predict future outcomes given control actions is fundamental for physical reasoning. However, such predictive models, often called world models, remains challenging to learn and are typically developed for task-specific…