Residual-based error bound for physics-informed neural networks

Neural networks are universal approximators and are studied for their use in solving differential equations. However, a major criticism is the lack of error bounds for obtained solutions. This paper proposes a technique to rigorously evaluate the error bound of Physics-Informed Neural Networks (PINNs) on most linear ordinary differential equations (ODEs), certain nonlinear ODEs, and first-order linear partial differential equations (PDEs). The error bound is based purely on equation structure and residual information and does not depend on assumptions of how well the networks are trained. We propose algorithms that bound the error efficiently. Some proposed algorithms provide tighter bounds than others at the cost of longer run time.Comment: 10 page main artichle + 5 page supplementary materia

Emerald Ash Borer and the application of biological control in Virginia

The emerald ash borer (Agrilus planipennis; EAB) is an invasive wood-boring beetle whose larvae feed on ash phloem. After only 1-5 years of infestation, the larvae create extensive tunnels under the bark that disrupt the tree’s ability to transport water and nutrients, which eventually girdles and kills the tree. Since 2008, EAB has spread to all but the eastern-most counties in Virginia. Bological control is one strategy to limit EAB populations. In this project we study control by native agents (woodpeckers) and imported agents (parasitoid wasps). Mathematical models of host-parasitoid interactions and simulations based on both models and field studies will be presented. Our novel contribution extends the basic Nicholson-Bailey model to a partial refuge system, realized in Virginia where EAB infests both ash and white fringetrees with fringetrees less attractive to the parasitoids. We determine ranges for model parameters that result in stable equilibrium populations

STL-SGD: Speeding Up Local SGD with Stagewise Communication Period

Distributed parallel stochastic gradient descent algorithms are workhorses for large scale machine learning tasks. Among them, local stochastic gradient descent (Local SGD) has attracted significant attention due to its low communication complexity. Previous studies prove that the communication complexity of Local SGD with a fixed or an adaptive communication period is in the order of $O (N^{\frac{3}{2}} T^{\frac{1}{2}})$ and $O (N^{\frac{3}{4}} T^{\frac{3}{4}})$ when the data distributions on clients are identical (IID) or otherwise (Non-IID), where $N$ is the number of clients and $T$ is the number of iterations. In this paper, to accelerate the convergence by reducing the communication complexity, we propose \textit{ST}agewise \textit{L}ocal \textit{SGD} (STL-SGD), which increases the communication period gradually along with decreasing learning rate. We prove that STL-SGD can keep the same convergence rate and linear speedup as mini-batch SGD. In addition, as the benefit of increasing the communication period, when the objective is strongly convex or satisfies the Polyak-\L ojasiewicz condition, the communication complexity of STL-SGD is $O (N \log{T})$ and $O (N^{\frac{1}{2}} T^{\frac{1}{2}})$ for the IID case and the Non-IID case respectively, achieving significant improvements over Local SGD. Experiments on both convex and non-convex problems demonstrate the superior performance of STL-SGD.Comment: Accepted by AAAI202

Multimodal N-of-1 trials: A Novel Personalized Healthcare Design

N-of-1 trials aim to estimate treatment effects on the individual level and can be applied to personalize a wide range of physical and digital interventions in mHealth. In this study, we propose and apply a framework for multimodal N-of-1 trials in order to allow the inclusion of health outcomes assessed through images, audio or videos. We illustrate the framework in a series of N-of-1 trials that investigate the effect of acne creams on acne severity assessed through pictures. For the analysis, we compare an expert-based manual labelling approach with different deep learning-based pipelines where in a first step, we train and fine-tune convolutional neural networks (CNN) on the images. Then, we use a linear mixed model on the scores obtained in the first step in order to test the effectiveness of the treatment. The results show that the CNN-based test on the images provides a similar conclusion as tests based on manual expert ratings of the images, and identifies a treatment effect in one individual. This illustrates that multimodal N-of-1 trials can provide a powerful way to identify individual treatment effects and can enable large-scale studies of a large variety of health outcomes that can be actively and passively assessed using technological advances in order to personalized health interventions

JAX-FEM: A differentiable GPU-accelerated 3D finite element solver for automatic inverse design and mechanistic data science

This paper introduces JAX-FEM, an open-source differentiable finite element method (FEM) library. Constructed on top of Google JAX, a rising machine learning library focusing on high-performance numerical computing, JAX-FEM is implemented with pure Python while scalable to efficiently solve problems with moderate to large sizes. For example, in a 3D tensile loading problem with 7.7 million degrees of freedom, JAX-FEM with GPU achieves around 10$\times$ acceleration compared to a commercial FEM code depending on platform. Beyond efficiently solving forward problems, JAX-FEM employs the automatic differentiation technique so that inverse problems are solved in a fully automatic manner without the need to manually derive sensitivities. Examples of 3D topology optimization of nonlinear materials are shown to achieve optimal compliance. Finally, JAX-FEM is an integrated platform for machine learning-aided computational mechanics. We show an example of data-driven multi-scale computations of a composite material where JAX-FEM provides an all-in-one solution from microscopic data generation and model training to macroscopic FE computations. The source code of the library and these examples are shared with the community to facilitate computational mechanics research

RNase A Inhibits Formation of Neutrophil Extracellular Traps in Subarachnoid Hemorrhage

Background: Subarachnoid hemorrhage (SAH) caused by rupture of an intracranial aneurysm, is a life-threatening emergency that is associated with substantial morbidity and mortality. Emerging evidence suggests involvement of the innate immune response in secondary brain injury, and a potential role of neutrophil extracellular traps (NETs) for SAH-associated neuroinflammation. In this study, we investigated the spatiotemporal patterns of NETs in SAH and the potential role of the RNase A (the bovine equivalent to human RNase 1) application on NET burden. Methods: A total number of n=81 male C57Bl/6 mice were operated utilizing a filament perforation model to induce SAH, and Sham operation was performed for the corresponding control groups. To confirm the bleeding and exclude stroke and intracerebral hemorrhage, the animals received MRI after 24h. Mice were treated with intravenous injection of RNase A (42 mu g/kg body weight) or saline solution for the control groups, respectively. Quadruple-immunofluorescence (IF) staining for cell nuclei (DAPI), F-actin (phalloidin), citrullinated H3, and neurons (NeuN) was analyzed by confocal imaging and used to quantify NET abundance in the subarachnoid space (SAS) and brain parenchyma. To quantify NETs in human SAH patients, cerebrospinal spinal fluid (CSF) and blood samples from day 1, 2, 7, and 14 after bleeding onset were analyzed for double-stranded DNA (dsDNA) via Sytox Green. Results: Neutrophil extracellular traps are released upon subarachnoid hemorrhage in the SAS on the ipsilateral bleeding site 24h after ictus. Over time, NETs showed progressive increase in the parenchyma on both ipsi- and contralateral site, peaking on day 14 in periventricular localization. In CSF and blood samples of patients with aneurysmal SAH, NETs also increased gradually over time with a peak on day 7. RNase application significantly reduced NET accumulation in basal, cortical, and periventricular areas. Conclusion: Neutrophil extracellular trap formation following SAH originates in the ipsilateral SAS of the bleeding site and spreads gradually over time to basal, cortical, and periventricular areas in the parenchyma within 14days. Intravenous RNase application abrogates NET burden significantly in the brain parenchyma, underpinning a potential role in modulation of the innate immune activation after SAH

Coordinated voltage control for improved power system voltage stability by incorporating the reactive power reserve from wind farms

The absorption and output characteristics of reactive power of the doubly-fed induction generator (DFIG) greatly influence the voltage stability of PCC (Point of Common Coupling) where the wind farms are integrated into the bulk power grid. This study proposes a reactive power compensation strategy for coordinated voltage control (CVC) of PCC with large-scale wind farms to achieve the expected voltage quality of the power grid through a minimum amount of control actions in emergencies. To this end, the mechanism of reactive power and voltage control inside DFIG is first analyzed. Then, the concept of reactive power reserve (RPR) sensitivity concerning control actions is introduced and an index of voltage stability margin is proposed to evaluate and analyze the distance between the current operating point and the voltage collapse point by analyzing the relationship between reactive power reserve and voltage stability margin. In the event of an emergency, critical reactive power reserves are obtained to reduce the dimension and complexity of the control problem. The sensitivity of reactive power reserve and the control are formulated into a convex quadratic programming problem to optimize the control strategies for voltage stability. The proposed technology has been validated on the IEEE 39-bus system