Gaussian Process (GP) regression is a popular nonparametric and probabilistic machine learning method. Notably, GPs have favorable characteristics for addressing some fundamental challenges that arise when combining learning algorithms with control. After a discussion of these challenges and a short tutorial on GP regression, I will present some of our recent results in GP-based learning...
Dynamical modeling of a process is essential to study its dynamical behavior and perform engineering studies such as control and optimization. With the ease of accessibility of data, learning models directly from the data have recently drawn much attention. Constructing simple and compact models describing complex nonlinear dynamics is also desirable for efficient engineering studies on modest...
Convolutional neural networks (CNNs) are frequently used for image generation, see for instance [1,2]. In this context it has been observed in practice that CNNs have a smoothing effect on images. While this is desirable for denoising it also leads to unwanted blurring of edges. In this talk we formalize this observation by rigorously showing that, under mild conditions, images generated from...
In the context of Koopman operator based analysis of dynamical systems, the generator of the Koopman semigroup is of central importance. Models for the Koopman generator can be used, among others, for system identification, coarse graining, and control of the system at hand.
Bounds for the approximation and estimation error in this context are paramount to a better understanding of the...
In this presentation we discuss new machine learning techniques suitable to solve ill-posed inverse problems. In particular, we deal with the task of reconstructing data from a collection of noisy measurements that are typically not enough to recover the ground-truth univocally. In this context, we propose a machine learning approach based on adversarial training based on optimal transport...
Breast Cancer is the deadliest and commonly diagnosed cancer in women globally. Early diagnosis and treatment of breast cancer increases the chance of a five-year survival rate by 99%. Recent technological and computational advancement have led to the discovery of machine learning algorithms for the analysis of complex data. Machine learning algorithms have been widely applied for the analysis...
Given a nonnegative matrix X and a factorization rank r, nonnegative matrix factorization (NMF) approximates the matrix X as the product of a nonnegative matrix W with r columns and a nonnegative matrix H with r rows. NMF has become a standard linear dimensionality reduction technique in data mining and machine learning. In this talk, we first introduce NMF and show how it can be used in...
Trigonometric functions can be evaluated efficiently based on the Fast Fourier Transform and related techniques.
The computational cost is $\mathcal O(N \log N)$, where $N$ is the number of given nodes. Feature maps based on such functions are therefore well suited for big data analysis, where the number of data points is typically very large.
However, the size of a full grid of Fourier...
In recent decades, non-intrusive model reduction has been developed to become a promising solution to system dynamics forecasting, especially in cases where data are collected from experimental campaigns or proprietary software simulations. Hence, the usage of non-intrusive modelling methods in combination with physics-based considerations could comprise a building block towards predictive...
Gaussian processes (GPs) are a crucial tool in machine learning and their use across different areas of science and engineering has increased given their ability to quantify the uncertainty in the model. The covariance matrices of GPs arise from kernel functions, which are crucial in many learning tasks and the matrices are typically dense and large-scale. Depending on their dimension even...
In recent years, machine learning has become a prevalent tool to
provide predictive models in many applications. In this talk, we are
interested in using such predictors to model relationships between
variables of an optimization model in Gurobi. For example, a
regression model may predict the demand of certain products as a
function of their prices and marketing budgets among other...
Spiking neural networks, also often referred to as the third generation of neural networks, carry the potential for a massive reduction in memory and energy consumption over traditional, second-generation neural networks. Inspired by the undisputed efficiency of the human brain, they introduce temporal and neuronal sparsity, which can be exploited by next-generation neuromorphic hardware. To...
This work is at the interface of reduced-order modeling, data assimilation and machine learning, in which we present a model that merges the Proper Orthogonal Decomposition (POD)-Galerkin reduction methodology with Physics Informed Neural Networks (PINNs) for the sake of solving inverse problems involving the Navier--Stokes equations (NSE).
The model constructs a POD-Galerkin ROM for the...
In the recent years, reinforcement learning (RL) has been identified as a potentially potent optimization method for stochastic control problems. The mathematical underpinning of RL is the Markov Decision Process (MDP), which provides a formal framework for devising policies for optimal decision making under uncertainties. While RL is just one method for finding such policies that solve the...
