Anoush Poursartip

Navid Zobeiry, Anoush Poursartip

Science-based simulation tools such as Finite Element (FE) models are routinely used in scientific and engineering applications. While their success is strongly dependent on our understanding of underlying governing physical laws, they suffer inherent limitations including trade-off between fidelity/accuracy and speed. The recent rise of Machine Learning (ML) proposes a theory-agnostic paradigm. In complex multi-physics problems, however, creating large enough datasets for successful training of ML models has proven to be challenging. One promising strategy to bridge the divide between these approaches and take advantage of their respective strengths is Theory-Guided Machine Learning (TGML) which aims to integrate physical laws into ML algorithms. In this paper, three case studies on thermal management during processing of advanced composites are presented and studied using FE, ML and TGML. A structured approach to incrementally adding increasingly complex physics to training of TGML model is presented. The benefits of TGML over ML models are seen in more accurate predictions, particularly outside the training region, and ability to train with small datasets. One benefit of TGML over FE is significant speed improvement to potentially develop real-time feedback systems. A recent successful implementation of a TGML model to assess producibility of aerospace composite parts is presented.

Sina Amini Niaki, Ehsan Haghighat, Trevor Campbell et al.

We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations -- including conductive heat transfer and resin cure kinetics -- by optimizing the parameters of a deep neural network (DNN) using a physics-based loss function. To account for the vastly different behaviour of thermal conduction and resin cure, we design a PINN consisting of two disconnected subnetworks, and develop a sequential training algorithm that mitigates instability present in traditional training methods. Further, we incorporate explicit discontinuities into the DNN at the composite-tool interface and enforce known physical behaviour directly in the loss function to improve the solution near the interface. We train the PINN with a technique that automatically adapts the weights on the loss terms corresponding to PDE, boundary, interface, and initial conditions. Finally, we demonstrate that one can include problem parameters as an input to the model -- resulting in a surrogate that provides real-time simulation for a range of problem settings -- and that one can use transfer learning to significantly reduce the training time for problem settings similar to that of an initial trained model. The performance of the proposed PINN is demonstrated in multiple scenarios with different material thicknesses and thermal boundary conditions.

Andreas Munk, Berend Zwartsenberg, Adam Ścibior et al.

We present a framework for automatically structuring and training fast, approximate, deep neural surrogates of stochastic simulators. Unlike traditional approaches to surrogate modeling, our surrogates retain the interpretable structure and control flow of the reference simulator. Our surrogates target stochastic simulators where the number of random variables itself can be stochastic and potentially unbounded. Our framework further enables an automatic replacement of the reference simulator with the surrogate when undertaking amortized inference. The fidelity and speed of our surrogates allow for both faster stochastic simulation and accurate and substantially faster posterior inference. Using an illustrative yet non-trivial example we show our surrogates' ability to accurately model a probabilistic program with an unbounded number of random variables. We then proceed with an example that shows our surrogates are able to accurately model a complex structure like an unbounded stack in a program synthesis example. We further demonstrate how our surrogate modeling technique makes amortized inference in complex black-box simulators an order of magnitude faster. Specifically, we do simulator-based materials quality testing, inferring safety-critical latent internal temperature profiles of composite materials undergoing curing.