Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be computationally demanding, especially for intricate functions like wavefields. This is primarily due to the neural-based (learned) basis functions, biased toward low frequencies, as they are dominated by polynomial calculations, which are not inherently wavefield-friendly. In response, we propose an approach to enhance the efficiency and accuracy of neural network wavefield solutions by modeling them as linear combinations of Gabor basis functions that satisfy the wave equation. Specifically, for the Helmholtz equation, we augment the fully connected neural network model with an adaptable Gabor layer constituting the final hidden layer, employing a weighted summation of these Gabor neurons to compute the predictions (output). These weights/coefficients of the Gabor functions are learned from the previous hidden layers that include nonlinear activation functions. To ensure the Gabor layer's utilization across the model space, we incorporate a smaller auxiliary network to forecast the center of each Gabor function based on input coordinates. Realistic assessments showcase the efficacy of this novel implementation compared to the vanilla PINN, particularly in scenarios involving high-frequencies and realistic models that are often challenging for PINNs.
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We consider the problem of using SciML to predict solutions of high Mach fluid flows over irregular geometries. In this setting, data is limited, and so it is desirable for models to perform well in the low-data setting. We show that Neural Basis Functions (NBF), which learns a basis of behavior modes from the data and then uses this basis to make predictions, is more effective than a basis-unaware baseline model. In addition, we identify continuing challenges in the space of predicting solutions for this type of problem.
As the Internet of Things (IoT) has become truly ubiquitous, so has the surrounding threat landscape. However, while the security of classical computing systems has significantly matured in the last decades, IoT cybersecurity is still typically low or fully neglected. This paper provides a classification of IoT malware. Major targets and used exploits for attacks are identified and referred to the specific malware. The lack of standard definitions of IoT devices and, therefore, security goals has been identified during this research as a profound barrier in advancing IoT cybersecurity. Furthermore, standardized reporting of IoT malware by trustworthy sources is required in the field. The majority of current IoT attacks continue to be of comparably low effort and level of sophistication and could be mitigated by existing technical measures.
An efficient mass lumping scheme for isogeometric analysis based on approximate dual basis functions
In this contribution, we provide a new mass lumping scheme for explicit dynamics in isogeometric analysis (IGA). To this end, an element formulation based on the idea of dual functionals is developed. Non-Uniform Rational B-splines (NURBS) are applied as shape functions and their corresponding dual basis functions are applied as test functions in the variational form, where two kinds of dual basis functions are compared. The first type are approximate dual basis functions (AD) with varying degree of reproduction, resulting in banded mass matrices. Dual basis functions derived from the inversion of the Gram matrix (IG) are the second type and already yield diagonal mass matrices. We will show that it is possible to apply the dual scheme as a transformation of the resulting system of equations based on NURBS as shape and test functions. Hence, it can be easily implemented into existing IGA routines. Treating the application of dual test functions as preconditioner reduces the additional computational effort, but it cannot entirely erase it and the density of the stiffness matrix still remains higher than in standard Bubnov-Galerkin formulations. In return applying additional row-sum lumping to the mass matrices is either not necessary for IG or the caused loss of accuracy is lowered to a reasonable magnitude in the case of AD. Numerical examples show a significantly better approximation of the dynamic behavior for the dual lumping scheme compared to standard NURBS approaches making use of row-sum lumping. Applying IG yields accurate numerical results without additional lumping. But as result of the global support of the IG dual basis functions, fully populated stiffness matrices occur, which are entirely unsuitable for explicit dynamic simulations. Combining AD and row-sum lumping leads to an efficient computation regarding effort and accuracy.
We present ParrotTTS, a modularized text-to-speech synthesis model leveraging disentangled self-supervised speech representations. It can train a multi-speaker variant effectively using transcripts from a single speaker. ParrotTTS adapts to a new language in low resource setup and generalizes to languages not seen while training the self-supervised backbone. Moreover, without training on bilingual or parallel examples, ParrotTTS can transfer voices across languages while preserving the speaker specific characteristics, e.g., synthesizing fluent Hindi speech using a French speaker's voice and accent. We present extensive results in monolingual and multi-lingual scenarios. ParrotTTS outperforms state-of-the-art multi-lingual TTS models using only a fraction of paired data as latter.
We analyze the wave equation in mixed form, with periodic and/or Dirichlet homogeneous boundary conditions, and nonconstant coefficients that depend on the spatial variable. For the discretization, the weak form of the second equation is replaced by a strong form, written in terms of a projection operator. The system of equations is discretized with B-splines forming a De Rham complex along with suitable commutative projectors for the approximation of the second equation. The discrete scheme is energy conservative when discretized in time with a conservative method such as Crank-Nicolson. We propose a convergence analysis of the method to study the dependence with respect to the mesh size $h$, with focus on the consistency error. Numerical results show optimal convergence of the error in energy norm, and a relative error in energy conservation for long-time simulations of the order of machine precision.
Climate hazards can cause major disasters when they occur simultaneously as compound hazards. To understand the distribution of climate risk and inform adaptation policies, scientists need to simulate a large number of physically realistic and spatially coherent events. Current methods are limited by computational constraints and the probabilistic spatial distribution of compound events is not given sufficient attention. The bottleneck in current approaches lies in modelling the dependence structure between variables, as inference on parametric models suffers from the curse of dimensionality. Generative adversarial networks (GANs) are well-suited to such a problem due to their ability to implicitly learn the distribution of data in high-dimensional settings. We employ a GAN to model the dependence structure for daily maximum wind speed, significant wave height, and total precipitation over the Bay of Bengal, combining this with traditional extreme value theory for controlled extrapolation of the tails. Once trained, the model can be used to efficiently generate thousands of realistic compound hazard events, which can inform climate risk assessments for climate adaptation and disaster preparedness. The method developed is flexible and transferable to other multivariate and spatial climate datasets.
Providing a promising pathway to link the human brain with external devices, Brain-Computer Interfaces (BCIs) have seen notable advancements in decoding capabilities, primarily driven by increasingly sophisticated techniques, especially deep learning. However, achieving high accuracy in real-world scenarios remains a challenge due to the distribution shift between sessions and subjects. In this paper we will explore the concept of online test-time adaptation (OTTA) to continuously adapt the model in an unsupervised fashion during inference time. Our approach guarantees the preservation of privacy by eliminating the requirement to access the source data during the adaptation process. Additionally, OTTA achieves calibration-free operation by not requiring any session- or subject-specific data. We will investigate the task of electroencephalography (EEG) motor imagery decoding using a lightweight architecture together with different OTTA techniques like alignment, adaptive batch normalization, and entropy minimization. We examine two datasets and three distinct data settings for a comprehensive analysis. Our adaptation methods produce state-of-the-art results, potentially instigating a shift in transfer learning for BCI decoding towards online adaptation.
A fully discrete semi-convex-splitting finite-element scheme with stabilization for a degenerate Cahn-Hilliard cross-diffusion system is analyzed. The system consists of parabolic fourth-order equations for the volume fraction of the fiber phase and the solute concentration, modeling pre-patterning of lymphatic vessel morphology. The existence of discrete solutions is proved, and it is shown that the numerical scheme is energy stable up to stabilization, conserves the solute mass, and preserves the lower and upper bounds of the fiber phase fraction. Numerical experiments in two space dimensions using FreeFEM illustrate the phase segregation and pattern formation.
Positron Emission Tomography (PET) enables functional imaging of deep brain structures, but the bulk and weight of current systems preclude their use during many natural human activities, such as locomotion. The proposed long-term solution is to construct a robotic system that can support an imaging system surrounding the subject's head, and then move the system to accommodate natural motion. This requires a system to measure the motion of the head with respect to the imaging ring, for use by both the robotic system and the image reconstruction software. We report here the design, calibration, and experimental evaluation of a parallel string encoder mechanism for sensing this motion. Our results indicate that with kinematic calibration, the measurement system can achieve accuracy within 0.5mm, especially for small motions.
We consider in this paper a numerical approximation of Poisson-Nernst-Planck-Navier- Stokes (PNP-NS) system. We construct a decoupled semi-discrete and fully discrete scheme that enjoys the properties of positivity preserving, mass conserving, and unconditionally energy stability. Then, we establish the well-posedness and regularity of the initial and (periodic) boundary value problem of the PNP-NS system under suitable assumptions on the initial data, and carry out a rigorous convergence analysis for the fully discretized scheme. We also present some numerical results to validate the positivity-preserving property and the accuracy of our scheme.
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