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the following areas: partial differential equations, inverse problems, numerical methods for PDEs, scientific computing; the ability and interest to work with both rigorous mathematical arguments and
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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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will consider techniques like flow matching, and use ideas from optimal transport and neural (stochastic) differential equations, invariant Kalman filtering and geometric numerical integration
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will start in Leiden, transfer after a year to Lund for two years, with a final year in Leiden. You will consider nonlinear wave equations with spatial inhomogeneities and use tools from dynamical
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transport and neural (stochastic) differential equations, invariant Kalman filtering and geometric numerical integration. The application areas will be chosen among the use cases of the aiD canter
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mathematical arguments, and a drive to improve these skills. Curiosity about chaos, nonlinear dynamics, and unpredictability. Solid foundations in linear algebra and differential equations. Proficiency in
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scientific knowledge, such as physical laws, differential equations, and domain-specific constraints, to model, simulate, and understand complex systems. The project will explore modern SciML methods
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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