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Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and…

In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a…

The increasing decentralization of power systems driven by a large number of renewable energy sources poses challenges in power flow optimization. Partially unknown power line properties can render model-based approaches unsuitable. With…

A new iterative algorithm for solving initial data inverse problems from partial observations has been recently proposed in Ramdani, Tucsnak and Weiss [15]. Based on the concept of observers (also called Luenberger observers), this…

The paper develops the Loewner approach for data-based modeling of a linear distributed-parameter system. This approach is applied to a controlled flexible beam model coupled with a spring-mass system. The original dynamical system is…

In Acousto-Electric tomography, the objective is to extract information about the interior electrical conductivity in a physical body from knowledge of the interior power density data generated from prescribed boundary conditions for the…

Growing concerns over data privacy and security highlight the importance of machine unlearning--removing specific data influences from trained models without full retraining. Techniques like Membership Inference Attacks (MIAs) are widely…

Unsupervised ensemble learning emerged to address the challenge of combining multiple learners' predictions without access to ground truth labels or additional data. This paradigm is crucial in scenarios where evaluating individual…

The optimal reconstruction of cosmic metric perturbations and other signals requires knowledge of their power spectra and other parameters. If these are not known a priori, they have to be measured simultaneously from the same data used for…

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The model is a version of a conditional variational auto-encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty…

This work develops a data-based construction of inverse dynamics for LTI systems. Specifically, the problem addressed here is to find an input sequence from the corresponding output sequence based on pre-collected input and output data. The…

A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using the Euler-Bernoulli beam equation. Given appropriate datasets, the model can be used to regress the analytical value of the…

Surface reconstruction is a fundamental problem in 3D graphics. In this paper, we propose a learning-based approach for implicit surface reconstruction from raw point clouds without normals. Our method is inspired by Gauss Lemma in…

Instruction data is crucial for improving the capability of Large Language Models (LLMs) to align with human-level performance. Recent research LIMA demonstrates that alignment is essentially a process where the model adapts instructions'…

Learning disentangled representations with variational autoencoders (VAEs) is often attributed to the regularisation component of the loss. In this work, we highlight the interaction between data and the reconstruction term of the loss as…

This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…

The Variational Auto-Encoder (VAE) is a simple, efficient, and popular deep maximum likelihood model. Though usage of VAEs is widespread, the derivation of the VAE is not as widely understood. In this tutorial, we will provide an overview…

Deep directed generative models have attracted much attention recently due to their expressive representation power and the ability of ancestral sampling. One major difficulty of learning directed models with many latent variables is the…

Incorporating unstructured data into physical models is a challenging problem that is emerging in data assimilation. Traditional approaches focus on well-defined observation operators whose functional forms are typically assumed to be…

We address the problem of unsupervised disentanglement of latent representations learnt via deep generative models. In contrast to current approaches that operate on the evidence lower bound (ELBO), we argue that statistical independence in…