Inverse problems & optimization
Finding unseen or optimal structures.
Key works
Full waveform inversion
Full waveform inversion reconstructs hidden defects from ultrasonic wave measurements: the material distribution is adapted until the simulated waves match the measured ones.
Measurement
Reconstruction
Regularization
The unknown defects can be described with immersed boundary parametrizations, and the scaled boundary finite element method makes the inversion highly parallel. Real transducers are captured by distributed source inversion, and a quantitative study compares full waveform inversion with the total focusing method and reverse time migration using experimental data.
Laser beam shaping
Laser beam shaping designs the laser's intensity profile to control melt pools and temperatures in powder bed fusion.
The beam shape can be optimized for the melt pool geometry, or inverse-designed to follow a prescribed temperature field. Bead-on-plate experiments show how well thermal simulations hold across beam shapes.
Dynamic topology optimization
Dynamic topology optimization designs structures under transient loads, such as waves. Its gradients come from an adjoint simulation that runs backward in time and needs the full forward history, which quickly exceeds available memory. A memory-efficient adjoint method removes this limit and enables billion-parameter optimization on a single GPU.
With a neural reparametrization of the design, the optimization also finds better local optima.
Publications
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A memory-efficient adjoint method to enable billion parameter optimization on a single GPU in dynamic problems
Removes the memory wall of transient adjoints, putting billion-parameter designs on one GPU.
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Reconstructing effective ultrasound transducer models via distributed source inversion
Reconstructs an effective transducer model from measured wavefields, without knowing the transducer's internals.
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Quantitative comparison of the total focusing method, reverse time migration, and full waveform inversion for ultrasonic imaging
Compares total focusing, reverse time migration and full waveform inversion on the same ultrasonic data.
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Full-waveform inversion via the scaled boundary finite element method
A scaled boundary formulation for inhomogeneous media that makes full waveform inversion highly parallel.
Code -
Shape optimization of embedded solids using implicit Vertex-Morphing
Optimizes the shape of complex solids on a fixed grid, avoiding mesh distortion and re-meshing.
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Immersed boundary parametrizations for full waveform inversion
Compares ways of parametrizing an unknown boundary when inverting wave measurements.
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Isogeometric multi-resolution full waveform inversion based on the finite cell method
Reconstructs geometry at several resolutions by combining splines with the finite cell method.
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Point cloud-based elastic reverse time migration for ultrasonic imaging of components with vertical surfaces
Images defects in components with vertical surfaces by reverse time migration on point-cloud geometry.