Jonathan Wittmer

Jonathan Wittmer, Jacob Badger, Hari Sundar et al.

PDE-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes that are required to accurately compute the PDE solution introduce an enormous number of parameters and require large scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time dependent PDEs, the adjoint method that is often employed to efficiently compute gradients and higher order derivatives requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing both the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for both the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior to show how the DIAS method can be affordably extended to large scale problems without the need of checkpointing and large memory.

Chen Kong, James Fort, Aria Kang et al.

The Aria Gen 2 Pilot Dataset (A2PD) is an egocentric multimodal open dataset captured using the state-of-the-art Aria Gen 2 glasses. To facilitate timely access, A2PD is released incrementally with ongoing dataset enhancements. The initial release features Dia'ane, our primary subject, who records her daily activities alongside friends, each equipped with Aria Gen 2 glasses. It encompasses five primary scenarios: cleaning, cooking, eating, playing, and outdoor walking. In each of the scenarios, we provide comprehensive raw sensor data and output data from various machine perception algorithms. These data illustrate the device's ability to perceive the wearer, the surrounding environment, and interactions between the wearer and the environment, while maintaining robust performance across diverse users and conditions. The A2PD is publicly available at projectaria.com, with open-source tools and usage examples provided in Project Aria Tools.

Hwan Goh, Sheroze Sheriffdeen, Jonathan Wittmer et al.

In recent years, the field of machine learning has made phenomenal progress in the pursuit of simulating real-world data generation processes. One notable example of such success is the variational autoencoder (VAE). In this work, with a small shift in perspective, we leverage and adapt VAEs for a different purpose: uncertainty quantification in scientific inverse problems. We introduce UQ-VAE: a flexible, adaptive, hybrid data/model-informed framework for training neural networks capable of rapid modelling of the posterior distribution representing the unknown parameter of interest. Specifically, from divergence-based variational inference, our framework is derived such that most of the information usually present in scientific inverse problems is fully utilized in the training procedure. Additionally, this framework includes an adjustable hyperparameter that allows selection of the notion of distance between the posterior model and the target distribution. This introduces more flexibility in controlling how optimization directs the learning of the posterior model. Further, this framework possesses an inherent adaptive optimization property that emerges through the learning of the posterior uncertainty.