Related papers: Image Inversion and Uncertainty Quantification for…
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to…
In this paper we study model reduction of linear and bilinear quadratic stochastic control problems with parameter uncertainties. Specifically, we consider slow-fast systems with unknown diffusion coefficient and study the convergence of…
Text-to-image diffusion models offer powerful image editing capabilities. To edit real images, many methods rely on the inversion of the image into Gaussian noise. A common approach to invert an image is to gradually add noise to the image,…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…
Diffusion reconstruction plays a critical role in various applications such as image editing, restoration, and style transfer. In theory, the reconstruction should be simple - it just inverts and regenerates images by numerically solving…
System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
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…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents…
In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the…
Taking uncertainty into account is crucial when making strategic decisions. To guard against the risk of adverse scenarios, traditional optimisation techniques incorporate uncertainty on the basis of prior knowledge on its distribution. In…
Use of generative models and deep learning for physics-based systems is currently dominated by the task of emulation. However, the remarkable flexibility offered by data-driven architectures would suggest to extend this representation to…
The present paper proposes a novel Bayesian, computational strategy in the context of model-based inverse problems in elastostatics. On one hand we attempt to provide probabilistic estimates of the material properties and their spatial…
The study of transverse optical pattern formation has been studied extensively in nonlinear optics, with a recent experimental interest in studying the phenomenon using cold atoms, which can undergo real-space self-organization. Here, we…
Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…
Neural networks have emerged as powerful tools across various applications, yet their decision-making process often remains opaque, leading to them being perceived as "black boxes." This opacity raises concerns about their interpretability…
Geophysical inversion attempts to estimate the distribution of physical properties in the Earth's interior from observations collected at or above the surface. Inverse problems are commonly posed as least-squares optimization problems in…