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1. Integral Autoencoder Network for Discretization-Invariant Learning

   Yong Zheng Ong; Zuowei Shen; Haizhao Yang (January 2022, Journal of machine learning research)

   Stefan Harmeling (Ed.)

   Discretization invariant learning aims at learning in the infinite-dimensional function spaces with the capacity to process heterogeneous discrete representations of functions as inputs and/or outputs of a learning model. This paper proposes a novel deep learning framework based on integral autoencoders (IAE-Net) for discretization invariant learning. The basic building block of IAE-Net consists of an encoder and a decoder as integral transforms with data-driven kernels, and a fully connected neural network between the encoder and decoder. This basic building block is applied in parallel in a wide multi-channel structure, which is repeatedly composed to form a deep and densely connected neural network with skip connections as IAE-Net. IAE-Net is trained with randomized data augmentation that generates training data with heterogeneous structures to facilitate the performance of discretization invariant learning. The proposed IAE-Net is tested with various applications in predictive data science, solving forward and inverse problems in scientific computing, and signal/image processing. Compared with alternatives in the literature, IAE-Net achieves state-of-the-art performance in existing 

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2. Physics-Informed Machine Learning for Calibrating Macroscopic Traffic Flow Models

   https://doi.org/10.1287/trsc.2024.0526  

   Tang, Yu; Jin, Li; Ozbay, Kaan (November 2024, Transportation Science)

   Well-calibrated traffic flow models are fundamental to understanding traffic phenomena and designing control strategies. Traditional calibration has been developed based on optimization methods. In this paper, we propose a novel physics-informed, learning-based calibration approach that achieves performances comparable to and even better than those of optimization-based methods. To this end, we combine the classical deep autoencoder, an unsupervised machine learning model consisting of one encoder and one decoder, with traffic flow models. Our approach informs the decoder of the physical traffic flow models and thus induces the encoder to yield reasonable traffic parameters given flow and speed measurements. We also introduce the denoising autoencoder into our method so that it can handle not only with normal data but also corrupted data with missing values. We verified our approach with a case study of Interstate 210 Eastbound in California. It turns out that our approach can achieve comparable performance to the-state-of-the-art calibration methods given normal data and outperform them given corrupted data with missing values. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: This study was supported by the National Science Foundation [Grant CMMI-1949710] and the C2SMART Research Center, a Tier 1 University Transportation Center. 

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3. Eco-PiNN: A Physics-informed Neural Network for Eco-toll Estimation

   https://doi.org/10.1137/1.9781611977653.ch94  

   Li, Yan; Yang, Mingzhou; Eagon, Matthew; Farhadloo, Majid; Xie, Yiqun; Northrop, William; Shekhar, Shashi (January 2023, Proceedings of the SIAM International Conference on Data Mining)

   The eco-toll estimation problem quantifies the expected environmental cost (e.g., energy consumption, exhaust emissions) for a vehicle to travel along a path. This problem is important for societal applications such as eco-routing, which aims to find paths with the lowest exhaust emissions or energy need. The challenges of this problem are threefold: (1) the dependence of a vehicle's eco-toll on its physical parameters; (2) the lack of access to data with eco-toll information; and (3) the influence of contextual information (i.e. the connections of adjacent segments in the path) on the eco-toll of road segments. Prior work on eco-toll estimation has mostly relied on pure data-driven approaches and has high estimation errors given the limited training data. To address these limitations, we propose a novel Eco-toll estimation Physics-informed Neural Network framework (Eco-PiNN) using three novel ideas, namely, (1) a physics-informed decoder that integrates the physical laws governing vehicle dynamics into the network, (2) an attention-based contextual information encoder, and (3) a physics-informed regularization to reduce overfitting. Experiments on real-world heavy-duty truck data show that the proposed method can greatly improve the accuracy of eco-toll estimation compared with state-of-the-art methods. *The full version of the paper can be accessed at https://arxiv.org/abs/2301.05739 

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4. Unpaired data training enables super-resolution confocal microscopy from low-resolution acquisitions

   https://doi.org/10.1364/OL.537713  

   Trujillo, Carlos; Thompson, Lauren; Skalli, Omar; Doblas, Ana (October 2024, Optics Letters)

   Supervised deep-learning models have enabled super-resolution imaging in several microscopic imaging modalities, increasing the spatial lateral bandwidth of the original input images beyond the diffraction limit. Despite their success, their practical application poses several challenges in terms of the amount of training data and its quality, requiring the experimental acquisition of large, paired databases to generate an accurate generalized model whose performance remains invariant to unseen data. Cycle-consistent generative adversarial networks (cycleGANs) are unsupervised models for image-to-image translation tasks that are trained on unpaired datasets. This paper introduces a cycleGAN framework specifically designed to increase the lateral resolution limit in confocal microscopy by training a cycleGAN model using low- and high-resolution unpaired confocal images of human glioblastoma cells. Training and testing performances of the cycleGAN model have been assessed by measuring specific metrics such as background standard deviation, peak-to-noise ratio, and a customized frequency content measure. Our cycleGAN model has been evaluated in terms of image fidelity and resolution improvement using a paired dataset, showing superior performance than other reported methods. This work highlights the efficacy and promise of cycleGAN models in tackling super-resolution microscopic imaging without paired training, paving the path for turning home-built low-resolution microscopic systems into low-cost super-resolution instruments by means of unsupervised deep learning. 

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5. Predicting 3D soft tissue dynamics from 2D imaging using physics informed neural networks

   https://doi.org/10.1038/s42003-023-04914-y  

   Movahhedi, Mohammadreza; Liu, Xin-Yang; Geng, Biao; Elemans, Coen; Xue, Qian; Wang, Jian-Xun; Zheng, Xudong (May 2023, Communications Biology)

   Abstract Tissue dynamics play critical roles in many physiological functions and provide important metrics for clinical diagnosis. Capturing real-time high-resolution 3D images of tissue dynamics, however, remains a challenge. This study presents a hybrid physics-informed neural network algorithm that infers 3D flow-induced tissue dynamics and other physical quantities from sparse 2D images. The algorithm combines a recurrent neural network model of soft tissue with a differentiable fluid solver, leveraging prior knowledge in solid mechanics to project the governing equation on a discrete eigen space. The algorithm uses a Long-short-term memory-based recurrent encoder-decoder connected with a fully connected neural network to capture the temporal dependence of flow-structure-interaction. The effectiveness and merit of the proposed algorithm is demonstrated on synthetic data from a canine vocal fold model and experimental data from excised pigeon syringes. The results showed that the algorithm accurately reconstructs 3D vocal dynamics, aerodynamics, and acoustics from sparse 2D vibration profiles. 

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