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In a recent article, we presented a framework to control nonlinear partial differential equations (PDEs) by means of Koopman operator based reduced models and concepts from switched systems. The main idea was to transform a control system…

Visual-inertial odometry (VIO) systems traditionally rely on filtering or optimization-based techniques for egomotion estimation. While these methods are accurate under nominal conditions, they are prone to failure during severe…

We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it…

Ensemble learning consistently improves the performance of multi-class classification through aggregating a series of base classifiers. To this end, data-independent ensemble methods like Error Correcting Output Codes (ECOC) attract…

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications…

Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (the analysis step) in the data assimilation method Ensemble…

Error Correcting Output Codes, ECOC, is an output representation method capable of discovering some of the errors produced in classification tasks. This paper describes the application of ECOC to the training of feed forward neural…

The loss landscape of Variational Quantum Neural Networks (VQNNs) is characterized by local minima that grow exponentially with increasing qubits. Because of this, it is more challenging to recover information from model gradients during…

Modern deep learning algorithms use variations of gradient descent as their main learning methods. Gradient descent can be understood as the simplest Ordinary Differential Equation (ODE) solver; namely, the Euler method applied to the…

We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…

We consider the problem of performing Bayesian inference for logistic regression using appropriate extensions of the ensemble Kalman filter. Two interacting particle systems are proposed that sample from an approximate posterior and prove…

This paper proposes an Online Control-Informed Learning (OCIL) framework, which employs the well-established optimal control and state estimation techniques in the field of control to solve a broad class of learning tasks in an online…

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

We propose an adaptive optimization algorithm for solving unconstrained scaled gradient flow problems that achieves fast convergence by controlling the optimization trajectory shape and the discretization step sizes. Under a broad class of…

This paper presents a novel method for autonomously enhancing deep neural network training. My approach employs an Evaluation Neural Network (ENN) trained via deep reinforcement learning to predict the performance of the target network. The…

The ensemble of deep neural networks has been shown, both theoretically and empirically, to improve generalization accuracy on the unseen test set. However, the high training cost hinders its efficiency since we need a sufficient number of…

This paper investigates the formulation and implementation of Bayesian inverse problems to learn input parameters of partial differential equations (PDEs) defined on manifolds. Specifically, we study the inverse problem of determining the…

Training networks consisting of biophysically accurate neuron models could allow for new insights into how brain circuits can organize and solve tasks. We begin by analyzing the extent to which the central algorithm for neural network…

Physics-informed machine learning frameworks such as Physics-Informed Neural Networks (PINNs) and Physics-Informed Extreme Learning Machines (PI-ELMs) have shown great promise for solving partial differential equations (PDEs) but struggle…