Efficient stochastic Hessian estimation for full waveform inversion

In this abstract we present a method that allows arbitrary elements of the approximate Hessian to be estimated simultaneously. Preliminary theoretical and numerical investigations suggest that the number of forward models required for this procedure does not increase with the number of shots. As the number of shots increases this means that the cost of estimating these approximate Hessian entries becomes negligible relative to the cost of calculating the gradient. The most obvious application would be to estimate the diagonal of the approximate hessian. This can then be used as a very inexpensive preconditioner for optimization procedures, such as the truncated Newton method

A phase field method for tomographic reconstruction from limited data.

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images

A phase field method for tomographic reconstruction from limited data

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images

Towards Large-Scale Learned Solvers for Parametric PDEs with Model-Parallel Fourier Neural Operators

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable approaches based on convolutional networks. Once trained, FNOs can achieve speed-ups of multiple orders of magnitude over conventional numerical PDE solvers. However, due to the high dimensionality of their input data and network weights, FNOs have so far only been applied to two-dimensional or small three-dimensional problems. To remove this limited problem-size barrier, we propose a model-parallel version of FNOs based on domain-decomposition of both the input data and network weights. We demonstrate that our model-parallel FNO is able to predict time-varying PDE solutions of over 3.2 billions variables on Summit using up to 768 GPUs and show an example of training a distributed FNO on the Azure cloud for simulating multiphase CO$_2$ dynamics in the Earth's subsurface

Intercomparison of the LASCO-C2, SECCHI-COR1, SECCHI-COR2, and Mk4 Coronagraphs

In order to assess the reliability and consistency of white-light coronagraph measurements, we report on quantitative comparisons between polarized brightness [pB] and total brightness [B] images taken by the following white-light coronagraphs: LASCO-C2 on SOHO, SECCHI-COR1 and -COR2 on STEREO, and the ground-based MLSO-Mk4. The data for this comparison were taken on 16 April 2007, when both STEREO spacecraft were within 3.1 deg. of Earths heliographic longitude, affording essentially the same view of the Sun for all of the instruments. Due to the difficulties of estimating stray-light backgrounds in COR1 and COR2, only Mk4 and C2 produce reliable coronal-hole values (but not at overlapping heights), and these cannot be validated without rocket flights or ground-based eclipse measurements. Generally, the agreement between all of the instruments pB values is within the uncertainties in bright streamer structures, implying that measurements of bright CMEs also should be trustworthy. Dominant sources of uncertainty and stray light are discussed, as is the design of future coronagraphs from the perspective of the experiences with these instruments