Dylan Randle

Blake Bullwinkel, Dylan Randle, Pavlos Protopapas et al. · harvard

Solutions to differential equations are of significant scientific and engineering relevance. Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving differential equations, but they lack a theoretical justification for the use of any particular loss function. This work presents Differential Equation GAN (DEQGAN), a novel method for solving differential equations using generative adversarial networks to "learn the loss function" for optimizing the neural network. Presenting results on a suite of twelve ordinary and partial differential equations, including the nonlinear Burgers', Allen-Cahn, Hamilton, and modified Einstein's gravity equations, we show that DEQGAN can obtain multiple orders of magnitude lower mean squared errors than PINNs that use $L_2$, $L_1$, and Huber loss functions. We also show that DEQGAN achieves solution accuracies that are competitive with popular numerical methods. Finally, we present two methods to improve the robustness of DEQGAN to different hyperparameter settings.

Dylan Randle, Pavlos Protopapas, David Sondak

Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving differential equations with unsupervised neural networks that applies Generative Adversarial Networks (GANs) to \emph{learn the loss function} for optimizing the neural network. We present empirical results showing that our method, which we call Differential Equation GAN (DEQGAN), can obtain multiple orders of magnitude lower mean squared errors than an alternative unsupervised neural network method based on (squared) $L_2$, $L_1$, and Huber loss functions. Moreover, we show that DEQGAN achieves solution accuracy that is competitive with traditional numerical methods. Finally, we analyze the stability of our approach and find it to be sensitive to the selection of hyperparameters, which we provide in the appendix. Code available at https://github.com/dylanrandle/denn. Please address any electronic correspondence to dylanrandle@alumni.harvard.edu.

Che Wang, Jeroen van Baar, Chaitanya Mitash et al.

This work demonstrates how autonomously learning aspects of robotic operation from sparsely-labeled, real-world data of deployed, engineered solutions at industrial scale can provide with solutions that achieve improved performance. Specifically, it focuses on multi-suction robot picking and performs a comprehensive study on the application of multi-modal visual encoders for predicting the success of candidate robotic picks. Picking diverse items from unstructured piles is an important and challenging task for robot manipulation in real-world settings, such as warehouses. Methods for picking from clutter must work for an open set of items while simultaneously meeting latency constraints to achieve high throughput. The demonstrated approach utilizes multiple input modalities, such as RGB, depth and semantic segmentation, to estimate the quality of candidate multi-suction picks. The strategy is trained from real-world item picking data, with a combination of multimodal pretrain and finetune. The manuscript provides comprehensive experimental evaluation performed over a large item-picking dataset, an item-picking dataset targeted to include partial occlusions, and a package-picking dataset, which focuses on containers, such as boxes and envelopes, instead of unpackaged items. The evaluation measures performance for different item configurations, pick scenes, and object types. Ablations help to understand the effects of in-domain pretraining, the impact of different modalities and the importance of finetuning. These ablations reveal both the importance of training over multiple modalities but also the ability of models to learn during pretraining the relationship between modalities so that during finetuning and inference, only a subset of them can be used as input.