Deepak Akhare

Deepak Akhare, Zeping Chen, Richard Gulotty et al.

Chemical vapor infiltration (CVI) is a widely adopted manufacturing technique used in producing carbon-carbon and carbon-silicon carbide composites. These materials are especially valued in the aerospace and automotive industries for their robust strength and lightweight characteristics. The densification process during CVI critically influences the final performance, quality, and consistency of these composite materials. Experimentally optimizing the CVI processes is challenging due to long experimental time and large optimization space. To address these challenges, this work takes a modeling-centric approach. Due to the complexities and limited experimental data of the isothermal CVI densification process, we have developed a data-driven predictive model using the physics-integrated neural differentiable (PiNDiff) modeling framework. An uncertainty quantification feature has been embedded within the PiNDiff method, bolstering the model's reliability and robustness. Through comprehensive numerical experiments involving both synthetic and real-world manufacturing data, the proposed method showcases its capability in modeling densification during the CVI process. This research highlights the potential of the PiNDiff framework as an instrumental tool for advancing our understanding, simulation, and optimization of the CVI manufacturing process, particularly when faced with sparse data and an incomplete description of the underlying physics.

Deepak Akhare, Tengfei Luo, Jian-Xun Wang

The hybrid neural differentiable models mark a significant advancement in the field of scientific machine learning. These models, integrating numerical representations of known physics into deep neural networks, offer enhanced predictive capabilities and show great potential for data-driven modeling of complex physical systems. However, a critical and yet unaddressed challenge lies in the quantification of inherent uncertainties stemming from multiple sources. Addressing this gap, we introduce a novel method, DiffHybrid-UQ, for effective and efficient uncertainty propagation and estimation in hybrid neural differentiable models, leveraging the strengths of deep ensemble Bayesian learning and nonlinear transformations. Specifically, our approach effectively discerns and quantifies both aleatoric uncertainties, arising from data noise, and epistemic uncertainties, resulting from model-form discrepancies and data sparsity. This is achieved within a Bayesian model averaging framework, where aleatoric uncertainties are modeled through hybrid neural models. The unscented transformation plays a pivotal role in enabling the flow of these uncertainties through the nonlinear functions within the hybrid model. In contrast, epistemic uncertainties are estimated using an ensemble of stochastic gradient descent (SGD) trajectories. This approach offers a practical approximation to the posterior distribution of both the network parameters and the physical parameters. Notably, the DiffHybrid-UQ framework is designed for simplicity in implementation and high scalability, making it suitable for parallel computing environments. The merits of the proposed method have been demonstrated through problems governed by both ordinary and partial differentiable equations.

Sanket Jantre, Deepak Akhare, Zhiyuan Wang et al.

Partial differential equations (PDEs) underpin the modeling of many natural and engineered systems. It can be convenient to express such models as neural PDEs rather than using traditional numerical PDE solvers by replacing part or all of the PDE's governing equations with a neural network representation. Neural PDEs are often easier to differentiate, linearize, reduce, or use for uncertainty quantification than the original numerical solver. They are usually trained on solution trajectories obtained by long-horizon rollout of the PDE solver. Here we propose a more sample-efficient data-augmentation strategy for generating neural PDE training data from a computer model by space-filling sampling of local "stencil" states. This approach removes a large degree of spatiotemporal redundancy present in trajectory data and oversamples states that may be rarely visited but help the neural PDE generalize across the state space. We demonstrate that accurate neural PDE stencil operators can be learned from synthetic training data generated by the computational equivalent of 10 timesteps' worth of numerical simulation. Accuracy is further improved if we assume access to a single full-trajectory simulation from the computer model, which is typically available in practice. Across several PDE systems, we show that our data-augmented stencil data yield better trained neural stencil operators, with clear performance gains compared with naively sampled stencil data from simulation trajectories. Finally, with only 10 solver steps' worth of augmented stencil data, our approach outperforms traditional ML emulators trained on thousands of trajectories in long-horizon rollout accuracy and stability.