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Deep learning of free boundary and Stefan problems
Jun 04, 2020
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at \url{https://github.com/PredictiveIntelligenceLab/DeepStefan}.
Multiphysics discovery with moving boundaries using Ensemble SINDy and Peridynamic Differential Operator
Mar 27, 2023
This study proposes a novel framework for learning the underlying physics of phenomena with moving boundaries. The proposed approach combines Ensemble SINDy and Peridynamic Differential Operator (PDDO) and imposes an inductive bias assuming the moving boundary physics evolve in its own corotational coordinate system. The robustness of the approach is demonstrated by considering various levels of noise in the measured data using the 2D Fisher-Stefan model. The confidence intervals of recovered coefficients are listed, and the uncertainties of the moving boundary positions are depicted by obtaining the solutions with the recovered coefficients. Although the main focus of this study is the Fisher-Stefan model, the proposed approach is applicable to any type of moving boundary problem with a smooth moving boundary front without a mushy region. The code and data for this framework is available at: https://github.com/alicanbekar/MB_PDDO-SINDy.
Mind Reading at Work: Cooperation without common ground
May 26, 2021
As Stefan Kopp and Nicole Kramer say in their recent paper[Frontiers in Psychology 12 (2021) 597], despite some very impressive demonstrations over the last decade or so, we still don't know how how to make a computer have a half decent conversation with a human. They argue that the capabilities required to do this include incremental joint co-construction and mentalizing. Although agreeing whole heartedly with their statement of the problem, this paper argues for a different approach to the solution based on the "new" AI of situated action.
Towards Robust Named Entity Recognition for Historic German
Jun 18, 2019
Recent advances in language modeling using deep neural networks have shown that these models learn representations, that vary with the network depth from morphology to semantic relationships like co-reference. We apply pre-trained language models to low-resource named entity recognition for Historic German. We show on a series of experiments that character-based pre-trained language models do not run into trouble when faced with low-resource datasets. Our pre-trained character-based language models improve upon classical CRF-based methods and previous work on Bi-LSTMs by boosting F1 score performance by up to 6%. Our pre-trained language and NER models are publicly available under https://github.com/stefan-it/historic-ner .
The JuliaConnectoR: a functionally oriented interface for integrating Julia in R
May 13, 2020
Like many groups considering the new programming language Julia, we faced the challenge of accessing the algorithms that we develop in Julia from R. Therefore, we developed the R package JuliaConnectoR, available from the CRAN repository and GitHub (https://github.com/stefan-m-lenz/JuliaConnectoR), in particular for making advanced deep learning tools available. For maintainability and stability, we decided to base communication between R and Julia on TCP, using an optimized binary format for exchanging data. Our package also specifically contains features that allow for a convenient interactive use in R. This makes it easy to develop R extensions with Julia or to simply call functionality from Julia packages in R. With its functionally oriented design, the JuliaConnectoR enables a clean programming style by avoiding state in Julia that is not visible in the R workspace. We illustrate the further features of our package with code examples, and also discuss advantages over the two alternative packages JuliaCall and XRJulia. Finally, we demonstrate the usage of the package with a more extensive example for employing neural ordinary differential equations, a recent deep learning technique that has received much attention. This example also provides more general guidance for integrating deep learning techniques from Julia into R.
NPTC-net: Narrow-Band Parallel Transport Convolutional Neural Network on Point Clouds
May 29, 2019
Convolution plays a crucial role in various applications in signal and image processing, analysis and recognition. It is also the main building block of convolution neural networks (CNNs). Designing appropriate convolution neural networks on manifold-structured point clouds can inherit and empower recent advances of CNNs to analyzing and processing point cloud data. However, one of the major challenges is to define a proper way to "sweep" filters through the point cloud as a natural generalization of the planar convolution and to reflect the point cloud's geometry at the same time. In this paper, we consider generalizing convolution by adapting parallel transport on the point cloud. Inspired by a triangulated surface based method [Stefan C. Schonsheck, Bin Dong, and Rongjie Lai, arXiv:1805.07857.], we propose the Narrow-Band Parallel Transport Convolution (NPTC) using a specifically defined connection on a voxelized narrow-band approximation of point cloud data. With that, we further propose a deep convolutional neural network based on NPTC (called NPTC-net) for point cloud classification and segmentation. Comprehensive experiments show that the proposed NPTC-net achieves similar or better results than current state-of-the-art methods on point clouds classification and segmentation.
A Novel Approach to Fast Image Filtering Algorithm of Infrared Images based on Intro Sort Algorithm
Jan 19, 2012
In this study we investigate the fast image filtering algorithm based on Intro sort algorithm and fast noise reduction of infrared images. Main feature of the proposed approach is that no prior knowledge of noise required. It is developed based on Stefan- Boltzmann law and the Fourier law. We also investigate the fast noise reduction approach that has advantage of less computation load. In addition, it can retain edges, details, text information even if the size of the window increases. Intro sort algorithm begins with Quick sort and switches to heap sort when the recursion depth exceeds a level based on the number of elements being sorted. This approach has the advantage of fast noise reduction by reducing the comparison time. It also significantly speed up the noise reduction process and can apply to real-time image processing. This approach will extend the Infrared images applications for medicine and video conferencing.
* 7 pages. arXiv admin note: substantial text with articles by Chih-Lung Lin et al.