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We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…

Machine learning algorithms have been successfully used to approximate nonlinear maps under weak assumptions on the structure and properties of the maps. We present deep neural networks using dense and convolutional layers to solve an…

We consider two approaches to modelling of cell metabolism of 6-mercaptopurine, which is one of the important chemotherapy drugs used for treating of acute lymphocytic leukemia: kinetic ordinary differential equations and random Boolean…

Dealing with Partially Observable Markov Decision Processes is notably a challenging task. We face an average-reward infinite-horizon POMDP setting with an unknown transition model, where we assume the knowledge of the observation model.…

Finite element analysis (FEA) has been widely used to generate simulations of complex and nonlinear systems. Despite its strength and accuracy, the limitations of FEA can be summarized into two aspects: a) running high-fidelity FEA often…

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Knee Osteoarthritis (OA) is a common musculoskeletal disorder in the United States. When diagnosed at early stages, lifestyle interventions such as exercise and weight loss can slow OA progression, but at later stages, only an invasive…

Predicting nutrient transport and salinity distribution is crucial for mitigating climate-related threats to agromaritime systems. Traditional PDE-based models can capture the physics of nutrient dispersion, salinity and water quality.…

Precision breast cancer (BC) risk assessment is crucial for developing individualized screening and prevention. Despite the promising potential of recent mammogram (MG) based deep learning models in predicting BC risk, they mostly overlook…

Clinicians need to predict patient outcomes with high accuracy as early as possible after disease inception. In this manuscript, we show that patient-to-patient variability sets a fundamental limit on outcome prediction accuracy for a…

A key appeal of the recently proposed Neural Ordinary Differential Equation (ODE) framework is that it seems to provide a continuous-time extension of discrete residual neural networks. As we show herein, though, trained Neural ODE models…

Irregular sampling intervals and missing values in real-world time series data present challenges for conventional methods that assume consistent intervals and complete data. Neural Ordinary Differential Equations (Neural ODEs) offer an…

Neural controlled differential equations (Neural CDEs) are a continuous-time extension of recurrent neural networks (RNNs), achieving state-of-the-art (SOTA) performance at modelling functions of irregular time series. In order to interpret…

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art…

We propose a learning-based robust predictive control algorithm that compensates for significant uncertainty in the dynamics for a class of discrete-time systems that are nominally linear with an additive nonlinear component. Such systems…

Oncology drug development starts with a dose escalation phase to find the maximal tolerable dose (MTD). Dose limiting toxicity (DLT) is the primary endpoint for dose escalation phase. Traditionally, model-based dose escalation trial designs…

Combinations of neural ODEs with recurrent neural networks (RNN), like GRU-ODE-Bayes or ODE-RNN are well suited to model irregularly observed time series. While those models outperform existing discrete-time approaches, no theoretical…

Structure determination is essential to a mechanistic understanding of diseases and the development of novel therapeutics. Machine-learning-based structure prediction methods have made significant advancements by computationally predicting…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

Purpose: To determine whether deep learning-based algorithms applied to breast MR images can aid in the prediction of occult invasive disease following the di- agnosis of ductal carcinoma in situ (DCIS) by core needle biopsy. Material and…