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Zhenggqi Gao, Dinghuai Zhang, Luca Daniel, Duane S. Boning

A rare event is defined by a low probability of occurrence. Accurate estimation of such small probabilities is of utmost importance across diverse domains. Conventional Monte Carlo methods are inefficient, demanding an exorbitant number of samples to achieve reliable estimates. Inspired by the exact sampling capabilities of normalizing flows, we revisit this challenge and propose normalizing flow assisted importance sampling, termed NOFIS. NOFIS first learns a sequence of proposal distributions associated with predefined nested subset events by minimizing KL divergence losses. Next, it estimates the rare event probability by utilizing importance sampling in conjunction with the last proposal. The efficacy of our NOFIS method is substantiated through comprehensive qualitative visualizations, affirming the optimality of the learned proposal distribution, as well as a series of quantitative experiments encompassing $10$ distinct test cases, which highlight NOFIS's superiority over baseline approaches.

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Zhengqi Gao, Fan-Keng Sun, Duane S. Boning

In this paper, we exploit a fundamental principle of analog electronic circuitry, Kirchhoff's current law, to introduce a unique class of neural network models that we refer to as KirchhoffNet. KirchhoffNet establishes close connections with message passing neural networks and continuous-depth networks. We demonstrate that even in the absence of any traditional layers (such as convolution, pooling, or linear layers), KirchhoffNet attains 98.86% test accuracy on the MNIST dataset, comparable with state of the art (SOTA) results. What makes KirchhoffNet more intriguing is its potential in the realm of hardware. Contemporary deep neural networks are conventionally deployed on GPUs. In contrast, KirchhoffNet can be physically realized by an analog electronic circuit. Moreover, we justify that irrespective of the number of parameters within a KirchhoffNet, its forward calculation can always be completed within 1/f seconds, with f representing the hardware's clock frequency. This characteristic introduces a promising technology for implementing ultra-large-scale neural networks.

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Chih-Yu Lai, Fan-Keng Sun, Zhengqi Gao, Jeffrey H. Lang, Duane S. Boning

Time series anomaly detection is challenging due to the complexity and variety of patterns that can occur. One major difficulty arises from modeling time-dependent relationships to find contextual anomalies while maintaining detection accuracy for point anomalies. In this paper, we propose a framework for unsupervised time series anomaly detection that utilizes point-based and sequence-based reconstruction models. The point-based model attempts to quantify point anomalies, and the sequence-based model attempts to quantify both point and contextual anomalies. Under the formulation that the observed time point is a two-stage deviated value from a nominal time point, we introduce a nominality score calculated from the ratio of a combined value of the reconstruction errors. We derive an induced anomaly score by further integrating the nominality score and anomaly score, then theoretically prove the superiority of the induced anomaly score over the original anomaly score under certain conditions. Extensive studies conducted on several public datasets show that the proposed framework outperforms most state-of-the-art baselines for time series anomaly detection.

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Jiaqi Gu, Zhengqi Gao, Chenghao Feng, Hanqing Zhu, Ray T. Chen, Duane S. Boning, David Z. Pan

Optical computing is an emerging technology for next-generation efficient artificial intelligence (AI) due to its ultra-high speed and efficiency. Electromagnetic field simulation is critical to the design, optimization, and validation of photonic devices and circuits. However, costly numerical simulation significantly hinders the scalability and turn-around time in the photonic circuit design loop. Recently, physics-informed neural networks have been proposed to predict the optical field solution of a single instance of a partial differential equation (PDE) with predefined parameters. Their complicated PDE formulation and lack of efficient parametrization mechanisms limit their flexibility and generalization in practical simulation scenarios. In this work, for the first time, a physics-agnostic neural operator-based framework, dubbed NeurOLight, is proposed to learn a family of frequency-domain Maxwell PDEs for ultra-fast parametric photonic device simulation. We balance the efficiency and generalization of NeurOLight via several novel techniques. Specifically, we discretize different devices into a unified domain, represent parametric PDEs with a compact wave prior, and encode the incident light via masked source modeling. We design our model with parameter-efficient cross-shaped NeurOLight blocks and adopt superposition-based augmentation for data-efficient learning. With these synergistic approaches, NeurOLight generalizes to a large space of unseen simulation settings, demonstrates 2-orders-of-magnitude faster simulation speed than numerical solvers, and outperforms prior neural network models by ~54% lower prediction error with ~44% fewer parameters. Our code is available at https://github.com/JeremieMelo/NeurOLight.

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Zhengqi Gao, Fan-Keng Sun, Mingran Yang, Sucheng Ren, Zikai Xiong, Marc Engeler, Antonio Burazer, Linda Wildling, Luca Daniel, Duane S. Boning

Data lies at the core of modern deep learning. The impressive performance of supervised learning is built upon a base of massive accurately labeled data. However, in some real-world applications, accurate labeling might not be viable; instead, multiple noisy labels (instead of one accurate label) are provided by several annotators for each data sample. Learning a classifier on such a noisy training dataset is a challenging task. Previous approaches usually assume that all data samples share the same set of parameters related to annotator errors, while we demonstrate that label error learning should be both annotator and data sample dependent. Motivated by this observation, we propose a novel learning algorithm. The proposed method displays superiority compared with several state-of-the-art baseline methods on MNIST, CIFAR-100, and ImageNet-100. Our code is available at: https://github.com/zhengqigao/Learning-from-Multiple-Annotator-Noisy-Labels.

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Fan-Keng Sun, Duane S. Boning

The ability to forecast far into the future is highly beneficial to many applications, including but not limited to climatology, energy consumption, and logistics. However, due to noise or measurement error, it is questionable how far into the future one can reasonably predict. In this paper, we first mathematically show that due to error accumulation, sophisticated models might not outperform baseline models for long-term forecasting. To demonstrate, we show that a non-parametric baseline model based on periodicity can actually achieve comparable performance to a state-of-the-art Transformer-based model on various datasets. We further propose FreDo, a frequency domain-based neural network model that is built on top of the baseline model to enhance its performance and which greatly outperforms the state-of-the-art model. Finally, we validate that the frequency domain is indeed better by comparing univariate models trained in the frequency v.s. time domain.

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Fan-Keng Sun, Christopher I. Lang, Duane S. Boning

In many cases, it is difficult to generate highly accurate models for time series data using a known parametric model structure. In response, an increasing body of research focuses on using neural networks to model time series approximately. A common assumption in training neural networks on time series is that the errors at different time steps are uncorrelated. However, due to the temporality of the data, errors are actually autocorrelated in many cases, which makes such maximum likelihood estimation inaccurate. In this paper, we propose to learn the autocorrelation coefficient jointly with the model parameters in order to adjust for autocorrelated errors. For time series regression, large-scale experiments indicate that our method outperforms the Prais-Winsten method, especially when the autocorrelation is strong. Furthermore, we broaden our method to time series forecasting and apply it with various state-of-the-art models. Results across a wide range of real-world datasets show that our method enhances performance in almost all cases.

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Kyongmin Yeo, Dylan E. C. Grullon, Fan-Keng Sun, Duane S. Boning, Jayant R. Kalagnanam

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of the unknown parameters from a time series dataset. We assume that the time series data set consists of an ensemble of trajectories for a range of the parameters. The learning task is formulated as a statistical inference problem by considering the unknown parameters as random variables. A variational inference method is employed to train a recurrent neural network jointly with a feedforward neural network for an approximately posterior distribution. The approximate posterior distribution makes an inference on a trajectory to identify the effects of the unknown parameters and a recurrent neural network makes a prediction by using the outcome of the inference. In the numerical experiments, it is shown that the proposed variational inference model makes a more accurate simulation compared to the standard recurrent neural networks. It is found that the proposed deep learning model is capable of correctly identifying the dimensions of the random parameters and learning a representation of complex time series data.

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