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This PhD project will investigate partial differential equations arising from kinetic models, with a particular focus on variational methods. The research will explore how variational structures
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of analysis of partial differential equations (PDEs). The PhD candidate will be supervised by Havva Yoldaş and co-supervised by Raphael Winter (Cardiff University). The research topics primarily revolves around
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Microlocal analysis explores the classical/quantum correspondence in partial differential equations (PDEs). For example, the concept of symbol quantisation in the theory of pseudodifferential
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Parametric integrators approximate solutions of (high-dimensional) partial differential equations by restricting the numerical approximation to a closed form that nonlinearly depends on, and is
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identifying real households or companies. But energy data is not like images or text: it consists of time series living on a physical network, governed by power-flow equations. Off-the-shelf generative models
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of an object or medium from measurements of waves that have propagated through it. Mathematically, such problems lead to large-scale nonlinear inverse problems governed by partial differential equations (PDEs
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new approach has emerged that integrates data and mathematical models through neural networks. This has led to the development of a method for solving partial differential equations (PDEs) known as
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differential equations that require careful modeling and analysis. Imaging optics involves the design and optimization of imaging systems, such as cameras and telescopes, to most accurately capture and reproduce
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differential equations (PDEs). Full-waveform inversion is a powerful approach to such problems, but its practical use is limited by the strong nonlinearity of the inverse problem and by the computational cost
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transfer across different robotic platforms and morphologies. More generally, the dynamics of a robot can be represented by a generic differential equation describing the evolution of its state (x) as a