High-level python abstractions for optimal checkpointing in inversion problems

Inversion and PDE-constrained optimization problems often rely on solving the adjoint problem to calculate the gradient of the objec- tive function. This requires storing large amounts of intermediate data, setting a limit to the largest problem that might be solved with a given amount of memory available. Checkpointing is an approach that can reduce the amount of memory required by redoing parts of the computation instead of storing intermediate results. The Revolve checkpointing algorithm o ers an optimal schedule that trades computational cost for smaller memory footprints. Integrat- ing Revolve into a modern python HPC code and combining it with code generation is not straightforward. We present an API that makes checkpointing accessible from a DSL-based code generation environment along with some initial performance gures with a focus on seismic applications

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

Learned multiphysics inversion with differentiable programming and machine learning

We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical ultrasound), regularization with learned priors, and learned neural surrogates for multiphase flow simulations. By integrating multiple layers of abstraction, our software is designed to be both readable and scalable. This allows researchers to easily formulate their problems in an abstract fashion while exploiting the latest developments in high-performance computing. We illustrate and demonstrate our design principles and their benefits by means of building a scalable prototype for permeability inversion from time-lapse crosswell seismic data, which aside from coupling of wave physics and multiphase flow, involves machine learning

Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

Increased CCL2, CCL3, CCL5, and IL-1β cytokine concentration in piriform cortex, hippocampus, and neocortex after pilocarpine-induced seizures

BACKGROUND: Cytokines and chemokines play an important role in the neuroinflammatory response to an initial precipitating injury such as status epilepticus (SE). These signaling molecules participate in recruitment of immune cells, including brain macrophages (microglia), as well as neuroplastic changes, deterioration of damaged tissue, and epileptogenesis. This study describes the temporal and brain region pattern expression of numerous cytokines, including chemokines, after pilocarpine-induced seizures and discusses them in the larger context of their potential involvement in the changes that precede the development of epilepsy. FINDINGS: Adult rats received pilocarpine to induce SE and 90 min after seizure onset were treated with diazepam to mitigate seizures. Rats were subsequently deeply anesthetized and brain regions (hippocampus, piriform cortex, neocortex, and cerebellum) were freshly dissected at 2, 6, and 24 h or 5 days after seizures. Using methodology identical to our previous studies, simultaneous assay of multiple cytokines (CCL2, CCL3, CCL5, interleukin IL-1β, tumor necrosis factor (TNF-α)), and vascular endothelial growth factor (VEGF) was performed and compared to control rats. These proteins were selected based on existing evidence implicating them in the epileptogenic progression. A robust increase in CCL2 and CCL3 concentrations in the hippocampus, piriform cortex, and neocortex was observed at all time-points. The concentrations peaked with a ~200-fold increase 24 h after seizures and were two orders of magnitude greater than the significant increases observed for CCL5 and IL-1β in the same brain structures. TNF-α levels were altered in the piriform cortex and neocortex (24 h) and in the hippocampus (5 days) after SE. CONCLUSIONS: Pilocarpine-induced status epilepticus causes a rapid increase of multiple cytokines in limbic and neocortical regions. Understanding the precise spatial and temporal pattern of cytokines and chemokine changes could provide more viable therapeutic targets to reduce, reverse, or prevent the development of epilepsy following a precipitating injury