Learning Physics Informed Neural ODEs With Partial Measurements

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.

A Vision for Cleaner Rivers: Harnessing Snapshot Hyperspectral Imaging to Detect Macro-Plastic Litter

Plastic waste entering the riverine harms local ecosystems leading to negative ecological and economic impacts. Large parcels of plastic waste are transported from inland to oceans leading to a global scale problem of floating debris fields. In this context, efficient and automatized monitoring of mismanaged plastic waste is paramount. To address this problem, we analyze the feasibility of macro-plastic litter detection using computational imaging approaches in river-like scenarios. We enable near-real-time tracking of partially submerged plastics by using snapshot Visible-Shortwave Infrared hyperspectral imaging. Our experiments indicate that imaging strategies associated with machine learning classification approaches can lead to high detection accuracy even in challenging scenarios, especially when leveraging hyperspectral data and nonlinear classifiers. All code, data, and models are available online: https://github.com/RIVeR-Lab/hyperspectral_macro_plastic_detection.

JointNET: A Deep Model for Predicting Active Sacroiliitis from Sacroiliac Joint Radiography

Purpose: To develop a deep learning model that predicts active inflammation from sacroiliac joint radiographs and to compare the success with radiologists. Materials and Methods: A total of 1,537 (augmented 1752) grade 0 SIJs of 768 patients were retrospectively analyzed. Gold-standard MRI exams showed active inflammation in 330 joints according to ASAS criteria. A convolutional neural network model (JointNET) was developed to detect MRI-based active inflammation labels solely based on radiographs. Two radiologists blindly evaluated the radiographs for comparison. Python, PyTorch, and SPSS were used for analyses. P<0.05 was considered statistically significant. Results: JointNET differentiated active inflammation from radiographs with a mean AUROC of 89.2 (95% CI:86.8%, 91.7%). The sensitivity was 69.0% (95% CI:65.3%, 72.7%) and specificity 90.4% (95% CI:87.8 % 92.9%). The mean accuracy was 90.2% (95% CI: 87.6%, 92.8%). The positive predictive value was 74.6% (95% CI: 72.5%, 76.7%) and negative predictive value was 87.9% (95% CI: 85.4%, 90.5%) when prevalence was considered 1%. Statistical analyses showed a significant difference between active inflammation and healthy groups (p<0.05). Radiologists accuracies were less than 65% to discriminate active inflammation from sacroiliac joint radiographs. Conclusion: JointNET successfully predicts active inflammation from sacroiliac joint radiographs, with superior performance to human observers.

Hybrid Neural Network Augmented Physics-based Models for Nonlinear Filtering

In this paper we present a hybrid neural network augmented physics-based modeling (APBM) framework for Bayesian nonlinear latent space estimation. The proposed APBM strategy allows for model adaptation when new operation conditions come into play or the physics-based model is insufficient (or incomplete) to properly describe the latent phenomenon. One advantage of the APBMs and our estimation procedure is the capability of maintaining the physical interpretability of estimated states. Furthermore, we propose a constraint filtering approach to control the neural network contributions to the overall model. We also exploit assumed density filtering techniques and cubature integration rules to present a flexible estimation strategy that can easily deal with nonlinear models and high-dimensional latent spaces. Finally, we demonstrate the efficacy of our methodology by leveraging a target tracking scenario with nonlinear and incomplete measurement and acceleration models, respectively.

Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.