A deep learning framework is developed for multiscale characterization of poroelastic media from full waveform data which is known as poroelastography. Special attention is paid to heterogeneous environments whose multiphase properties may drastically change across several scales. Described in space-frequency, the data takes the form of focal solid displacement and pore pressure fields in various neighborhoods furnished either by reconstruction from remote data or direct measurements depending on the application. The objective is to simultaneously recover the six hydromechanical properties germane to Biot equations and their spatial distribution in a robust and efficient manner. Two major challenges impede direct application of existing state-of-the-art techniques for this purpose: (i) the sought-for properties belong to vastly different and potentially uncertain scales, and~(ii) the loss function is multi-objective and multi-scale (both in terms of its individual components and the total loss). To help bridge the gap, we propose the idea of \emph{network scaling} where the neural property maps are constructed by unit shape functions composed into a scaling layer. In this model, the unknown network parameters (weights and biases) remain of O(1) during training. This forms the basis for explicit scaling of the loss components and their derivatives with respect to the network parameters. Thereby, we propose the physics-based \emph{dynamic scaling} approach for adaptive loss balancing. The idea is first presented in a generic form for multi-physics and multi-scale PDE systems, and then applied through a set of numerical experiments to poroelastography. The results are presented along with reconstructions by way of gradient normalization (GradNorm) and Softmax adaptive weights (SoftAdapt) for loss balancing. A comparative analysis of the methods and corresponding results is provided.

Model compression is a ubiquitous tool that brings the power of modern deep learning to edge devices with power and latency constraints. The goal of model compression is to take a large reference neural network and output a smaller and less expensive compressed network that is functionally equivalent to the reference. Compression typically involves pruning and/or quantization, followed by re-training to maintain the reference accuracy. However, it has been observed that compression can lead to a considerable mismatch in the labels produced by the reference and the compressed models, resulting in bias and unreliability. To combat this, we present a framework that uses a teacher-student learning paradigm to better preserve labels. We investigate the role of additional terms to the loss function and show how to automatically tune the associated parameters. We demonstrate the effectiveness of our approach both quantitatively and qualitatively on multiple compression schemes and accuracy recovery algorithms using a set of 8 different real-world network architectures. We obtain a significant reduction of up to 4.1X in the number of mismatches between the compressed and reference models, and up to 5.7X in cases where the reference model makes the correct prediction.

Mehmood 3 asif.mehmood.1@us.af.mil Abstract Adaptive loss function formulation is an active area of research and has gained a great deal of popularity in recent years, following the success of deep learning. However, existing frameworks of adaptive loss functions often suffer from slow convergence and poor choice of weights for the loss components. Traditionally, the elements of a multi-part loss function are weighted equally or their weights are determined through heuristic approaches that yield near-optimal (or sub-optimal) results. T o address this problem, we propose a family of methods, called SoftAdapt, that dynamically change function weights for multi-part loss functions based on live performance statistics of the component losses. SoftAdapt is mathematically intuitive, computationally efficient and straightforward to implement. In this paper, we present the mathematical formulation and pseudocode for SoftAdapt, along with results from applying our methods to image reconstruction (Sparse Autoen-coders) and synthetic data generation (Introspective V aria-tional Autoencoders). 1. Introduction Almost all learning through neural networks require (i) a model describing the underlying structure of the training data, (ii) a loss function that gives a metric of how well the network is performing, and (iii) the optimization of the parameters to minimize the objective function.