Constraint-aware neural networks for Riemann problems

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Random matrix methods for high-dimensional machine learning models

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In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

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Mitigating Object Dependencies: Improving Point Cloud Self-Supervised Learning through Object Exchange

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In the realm of point cloud scene understanding, particularly in indoor scenes, objects are arranged following human habits, resulting in objects of certain semantics being closely positioned and displaying notable inter-object correlations. This can creat ...

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Biophysically accurate and machine learning-based surrogate models to optimize neuroprosthesis design and operation

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Electrical stimulation of the nervous system has emerged as a promising assistive technology in case of many injuries and illnesses across various parts of the nervous system. In particular, the invasive neuromodulation of the peripheral nervous system see ...

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Statistical Inference for Inverse Problems: From Sparsity-Based Methods to Neural Networks

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In inverse problems, the task is to reconstruct an unknown signal from its possibly noise-corrupted measurements. Penalized-likelihood-based estimation and Bayesian estimation are two powerful statistical paradigms for the resolution of such problems. They ...

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Scalable constrained optimization

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Modern optimization is tasked with handling applications of increasingly large scale, chiefly due to the massive amounts of widely available data and the ever-growing reach of Machine Learning. Consequently, this area of research is under steady pressure t ...

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The time-domain Cartesian multipole expansion of electromagnetic fields

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Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

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Safe Deep Neural Networks

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The capabilities of deep learning systems have advanced much faster than our ability to understand them. Whilst the gains from deep neural networks (DNNs) are significant, they are accompanied by a growing risk and gravity of a bad outcome. This is troubli ...

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Toward Wearable Biosensing by Spectroscopy-free Raman Shift Detection and Soft Optofluidics

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This thesis introduces spectroscopy-free Raman biosensing, which may find increasing use in the next generation of wearable devices for preventive healthcare. While wearables have made substantial advancements in detecting physical biomarkers, they have ye ...

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SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

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In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

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Generalization of Scaled Deep ResNets in the Mean-Field Regime

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Despite the widespread empirical success of ResNet, the generalization properties of deep ResNet are rarely explored beyond the lazy training regime. In this work, we investigate scaled ResNet in the limit of infinitely deep and wide neural networks, of wh ...

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