Willie J. Padilla

Simiao Ren, Saad Lahrichi, Yang Deng et al.

Deep active learning (DAL) methods have shown significant improvements in sample efficiency compared to simple random sampling. While these studies are valuable, they nearly always assume that optimal DAL hyperparameter (HP) settings are known in advance, or optimize the HPs through repeating DAL several times with different HP settings. Here, we argue that in real-world settings, or in the wild, there is significant uncertainty regarding good HPs, and their optimization contradicts the premise of using DAL (i.e., we require labeling efficiency). In this study, we evaluate the performance of eleven modern DAL methods on eight benchmark problems as we vary a key HP shared by all methods: the pool ratio. Despite adjusting only one HP, our results indicate that eight of the eleven DAL methods sometimes underperform relative to simple random sampling and some frequently perform worse. Only three methods always outperform random sampling (albeit narrowly), and we find that these methods all utilize diversity to select samples - a relatively simple criterion. Our findings reveal the limitations of existing DAL methods when deployed in the wild, and present this as an important new open problem in the field.

Darui Lu, Yang Deng, Jordan M. Malof et al.

Large language models (LLMs) such as ChatGPT, Gemini, LlaMa, and Claude are trained on massive quantities of text parsed from the internet and have shown a remarkable ability to respond to complex prompts in a manner often indistinguishable from humans. For all-dielectric metamaterials consisting of unit cells with four elliptical resonators, we present a LLM fine-tuned on up to 40,000 data that can predict the absorptivity spectrum given a text prompt that only specifies the metasurface geometry. Results are compared to conventional machine learning approaches including feed-forward neural networks, random forest, linear regression, and K-nearest neighbor (KNN). Remarkably, the fine-tuned LLM (FT-LLM) achieves a comparable performance across large dataset sizes with a deep neural network. We also explore inverse problems by asking the LLM to predict the geometry necessary to achieve a desired spectrum. LLMs possess several advantages over humans that may give them benefits for research, including the ability to process enormous amounts of data, find hidden patterns in data, and operate in higher-dimensional spaces. This suggests they may be able to leverage their general knowledge of the world to learn faster from training data than traditional models, making them valuable tools for research and analysis.

Simiao Ren, Yang Deng, Willie J. Padilla et al.

Deep learning (DL) is revolutionizing the scientific computing community. To reduce the data gap, active learning has been identified as a promising solution for DL in the scientific computing community. However, the deep active learning (DAL) literature is dominated by image classification problems and pool-based methods. Here we investigate the robustness of pool-based DAL methods for scientific computing problems (dominated by regression) where DNNs are increasingly used. We show that modern pool-based DAL methods all share an untunable hyperparameter, termed the pool ratio, denoted $γ$, which is often assumed to be known apriori in the literature. We evaluate the performance of five state-of-the-art DAL methods on six benchmark problems if we assume $γ$ is \textit{not} known - a more realistic assumption for scientific computing problems. Our results indicate that this reduces the performance of modern DAL methods and that they sometimes can even perform worse than random sampling, creating significant uncertainty when used in real-world settings. To overcome this limitation we propose, to our knowledge, the first query synthesis DAL method for regression, termed NA-QBC. NA-QBC removes the sensitive $γ$ hyperparameter and we find that, on average, it outperforms the other DAL methods on our benchmark problems. Crucially, NA-QBC always outperforms random sampling, providing more robust performance benefits.

Simiao Ren, Ashwin Mahendra, Omar Khatib et al.

Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but to compare, contrast, and evaluate assorted techniques it is critical to clarify the underlying ill-posedness of inverse problems. Here we review state-of-the-art approaches and present a comprehensive survey of deep learning inverse methods and invertible and conditional invertible neural networks to AEM design. We produce easily accessible and rapidly implementable AEM design benchmarks, which offers a methodology to efficiently determine the DL technique best suited to solving different design challenges. Our methodology is guided by constraints on repeated simulation and an easily integrated metric, which we propose expresses the relative ill-posedness of any AEM design problem. We show that as the problem becomes increasingly ill-posed, the neural adjoint with boundary loss (NA) generates better solutions faster, regardless of simulation constraints. On simpler AEM design tasks, direct neural networks (NN) fare better when simulations are limited, while geometries predicted by mixture density networks (MDN) and conditional variational auto-encoders (VAE) can improve with continued sampling and re-simulation.

Juncheng Dong, Simiao Ren, Yang Deng et al.

Numerous physical systems are described by ordinary or partial differential equations whose solutions are given by holomorphic or meromorphic functions in the complex domain. In many cases, only the magnitude of these functions are observed on various points on the purely imaginary jw-axis since coherent measurement of their phases is often expensive. However, it is desirable to retrieve the lost phases from the magnitudes when possible. To this end, we propose a physics-infused deep neural network based on the Blaschke products for phase retrieval. Inspired by the Helson and Sarason Theorem, we recover coefficients of a rational function of Blaschke products using a Blaschke Product Neural Network (BPNN), based upon the magnitude observations as input. The resulting rational function is then used for phase retrieval. We compare the BPNN to conventional deep neural networks (NNs) on several phase retrieval problems, comprising both synthetic and contemporary real-world problems (e.g., metamaterials for which data collection requires substantial expertise and is time consuming). On each phase retrieval problem, we compare against a population of conventional NNs of varying size and hyperparameter settings. Even without any hyper-parameter search, we find that BPNNs consistently outperform the population of optimized NNs in scarce data scenarios, and do so despite being much smaller models. The results can in turn be applied to calculate the refractive index of metamaterials, which is an important problem in emerging areas of material science.

Simiao Ren, Willie Padilla, Jordan Malof

We consider the task of solving generic inverse problems, where one wishes to determine the hidden parameters of a natural system that will give rise to a particular set of measurements. Recently many new approaches based upon deep learning have arisen generating impressive results. We conceptualize these models as different schemes for efficiently, but randomly, exploring the space of possible inverse solutions. As a result, the accuracy of each approach should be evaluated as a function of time rather than a single estimated solution, as is often done now. Using this metric, we compare several state-of-the-art inverse modeling approaches on four benchmark tasks: two existing tasks, one simple task for visualization and one new task from metamaterial design. Finally, inspired by our conception of the inverse problem, we explore a solution that uses a deep learning model to approximate the forward model, and then uses backpropagation to search for good inverse solutions. This approach, termed the neural-adjoint, achieves the best performance in many scenarios.