Zeda Xu

Zeda Xu, John Liechty, Sebastian Benthall et al.

Volatility, which indicates the dispersion of returns, is a crucial measure of risk and is hence used extensively for pricing and discriminating between different financial investments. As a result, accurate volatility prediction receives extensive attention. The Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model and its succeeding variants are well established models for stock volatility forecasting. More recently, deep learning models have gained popularity in volatility prediction as they demonstrated promising accuracy in certain time series prediction tasks. Inspired by Physics-Informed Neural Networks (PINN), we constructed a new, hybrid Deep Learning model that combines the strengths of GARCH with the flexibility of a Long Short-Term Memory (LSTM) Deep Neural Network (DNN), thus capturing and forecasting market volatility more accurately than either class of models are capable of on their own. We refer to this novel model as a GARCH-Informed Neural Network (GINN). When compared to other time series models, GINN showed superior out-of-sample prediction performance in terms of the Coefficient of Determination ($R^2$), Mean Squared Error (MSE), and Mean Absolute Error (MAE).

Zeda Xu, Nikolas Martelaro, Christopher McComb

The engineering design research community has studied agentic AI systems that use Large Language Model (LLM) agents to automate the engineering design process. However, these systems are prone to some of the same pathologies that plague humans. Just as human designers, LLM design agents can fixate on existing paradigms and fail to explore alternatives when solving design challenges, potentially leading to suboptimal solutions. In this work, we propose (1) a novel Self-Regulation Loop (SRL), in which the Design Agent self-regulates and explicitly monitors its own metacognition, and (2) a novel Co-Regulation Design Agentic Loop (CRDAL), in which a Metacognitive Co-Regulation Agent assists the Design Agent in metacognition to mitigate design fixation, thereby improving system performance for engineering design tasks. In the battery pack design problem examined here, we found that the novel CRDAL system generates designs with better performance, without significantly increasing the computational cost, compared to a plain Ralph Wiggum Loop (RWL) and the metacognitively self-assessing Self-Regulation Loop (SRL). Also, we found that the CRDAL system navigated through the latent design space more effectively than both SRL and RWL. However, the SRL did not generate designs with significantly better performance than RWL, even though it explored a different region of the design space. The proposed system architectures and findings of this work provide practical implications for future development of agentic AI systems for engineering design.

Jiangce Chen, Wenzhuo Xu, Zeda Xu et al.

Time-dependent partial differential equations (PDEs) for classic physical systems are established based on the conservation of mass, momentum, and energy, which are ubiquitous in scientific and engineering applications. These PDEs are strictly local-dependent according to the principle of locality in physics, which means that the evolution at a point is only influenced by the neighborhood around it whose size is determined by the length of timestep multiplied with the speed of characteristic information traveling in the system. However, deep learning architecture cannot strictly enforce the local-dependency as it inevitably increases the scope of information to make local predictions as the number of layers increases. Under limited training data, the extra irrelevant information results in sluggish convergence and compromised generalizability. This paper aims to solve this problem by proposing a data decomposition method to strictly limit the scope of information for neural operators making local predictions, which is called data decomposition enforcing local-dependency (DDELD). The numerical experiments over multiple physical phenomena show that DDELD significantly accelerates training convergence and reduces test errors of benchmark models on large-scale engineering simulations.