Machine learning has found its way into almost every area of science and engineering, and we are only at the beginning of its exploration across fields. Being a popular, versatile and powerful framework, machine learning has proven most useful where classical techniques are computationally inefficient, which applies particularly to computational solid mechanics. Here, we dare to give a non-exhaustive

Spatial symmetries and invariances play an important role in the description of materials. When modelling material properties, it is important to be able to respect such invariances. Here we discuss how to model and generate random ensembles of tensors where one wants to be able to prescribe certain classes of spatial symmetries and invariances for the whole ensemble, while at the same time demanding

Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed-form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches. First, physics-informed neural networks

High resolution crop type maps are an important tool for improving food security, and remote sensing is increasingly used to create such maps in regions that possess ground truth labels for model training. However, these labels are absent in many regions, and models trained in other regions on typical satellite features, such as those from optical sensors, often exhibit low performance when transferred

Simulation experiments are typically conducted repeatedly during the model development process, for example, to re-validate if a behavioral property still holds after several model changes. Approaches for automatically reusing and generating simulation experiments can support modelers in conducting simulation studies in a more systematic and effective manner. They rely on explicit experiment specifications

The financial time series analysis is important access to touch the complex laws of financial markets. Among many goals of the financial time series analysis, one is to construct a model that can extract the information of the future return out of the known historical stock data, such as stock price, financial news, and e.t.c. To design such a model, prior knowledge on how the future return is correlated

This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite element toolbox, Gridap in Julia. The present work exploits the advantages of both the phase-field model and Gridap toolbox for simulating fracture in brittle materials. On one hand, the use of the phase-field model, which is a continuum approach and uses a diffuse representation

Motivation: Omics data, such as transcriptomics or phosphoproteomics, are broadly used to get a snap-shot of the molecular status of cells. In particular, changes in omics can be used to estimate the activity of pathways, transcription factors and kinases based on known regulated targets, that we call footprints. Then the molecular paths driving these activities can be estimated using causal reasoning

Variational phase-field methods have been shown powerful for the modeling of complex crack propagation without a priori knowledge of the crack path or ad hoc criteria. However, phase-field models suffer from their energy functional being non-linear and non-convex, while requiring a very fine mesh to capture the damage gradient. This implies a high computational cost, limiting concrete engineering applications

The Linac Coherent Light Source (LCLS) is an X- ray free electron laser (XFEL) facility enabling the study of the structure and dynamics of single macromolecules. A major upgrade will bring the repetition rate of the X-ray source from 120 to 1 million pulses per second. Exascale high performance computing (HPC) capabilities will be required to process the corresponding data rates. We present SpiniFEL

Hybrid modeling, the combination of first principle and machine learning models, is an emerging research field that gathers more and more attention. Even if hybrid models produce formidable results for academic examples, there are still different technical challenges that hinder the use of hybrid modeling in real-world applications. By presenting NeuralFMUs, the fusion of a FMU, a numerical ODE solver

We demonstrate an adaptive sampling approach for computing the probability of a rare event for a set of three-dimensional airplane geometries under various flight conditions. We develop a fully automated method to generate parameterized airplanes geometries and create volumetric mesh for viscous CFD solution. With the automatic geometry and meshing, we perform the adaptive sampling procedure to compute

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the given parametric surfaces. Each pyramid serves as an integration cell with a geometric mapping from a standard parent domain (e.g., a unit cube),

The analysis of differential gene expression from RNA-Seq data has become a standard for several research areas mainly involving bioinformatics. The steps for the computational analysis of these data include many data types and file formats, and a wide variety of computational tools that can be applied alone or together as pipelines. This paper presents a review of differential expression analysis

This paper presents the first time implementation of the eXtended Finite Element Method (XFEM) in the general purpose commercial software COMSOL Multiphysics. An enrichment strategy is proposed, consistent with the structure of the software. To this end, for each set of enrichment functions, an additional Solid Mechanics module is incorporated into the numerical framework, coupled with compatible modifications

Surrogate models have several uses in engineering design, including speeding up design optimization, noise reduction, test measurement interpolation, gradient estimation, portability, and protection of intellectual property. Traditionally, surrogate models require that all training data conform to the same parametrization (e.g. design variables), limiting design freedom and prohibiting the reuse of

Length scale control is imposed in topology optimization (TO) to make designs amenable to manufacturing and other functional requirements. Broadly, there are two types of length-scale control in TO: \emph {exact} and \emph {approximate}. While the former is desirable, its implementation can be difficult, and is computationally expensive. Approximate length scale control is therefore preferred, and

This article discusses a mixed FE technique for 3D nonlinear elasticity using a Hu-Washizu (HW) type variational principle. Here, the deformed configuration and sections from its cotangent bundle are taken as additional input arguments. The critical points of the HW functional enforce compatibility of these sections with the configuration, in addition to mechanical equilibrium and constitutive relations

This paper introduces the full Low-carbon Expansion Generation Optimization (LEGO) model available on Github (https://github.com/wogrin/LEGO). LEGO is a mixed-integer quadratically constrained optimization problem and has been designed to be a multi-purpose tool, like a Swiss army knife, that can be employed to study many different aspects of the energy sector. Ranging from short-term unit commitment

The last decade has witnessed the emergence of magneto-active polymers (MAPs) as one of the most advanced multi-functional soft composites. Depending on the magnetisation mechanisms and responsive behaviour, MAPs are mainly classified into two groups: i) hard magnetic MAPs in which a large residual magnetic flux density sustains even after the removal of the external magnetic field, and ii) soft magnetic

The properties of a thermally sprayed coating, such as its durability or thermal conductivity depend on its microstructure, which is in turn directly related to the particle impact process. To simulate this process we present a 3D Smoothed Particle Hydrodynamics (SPH) model, which represents the molten droplet as an incompressible fluid, while a semi-implicit Enthalpy-Porosity method is applied for

While the application of the Smoothed Particle Hydrodynamics (SPH) method for the modeling of welding processes has become increasingly popular in recent years, little is yet known about the quantitative predictive capability of this method. We propose a novel SPH model for the simulation of the tungsten inert gas (TIG) spot welding process and conduct a thorough comparison between our SPH implementation

Active structures have the ability to change their shape, properties, and functionality as a response to changing operational conditions, which makes them more versatile than their static counterparts. However, most active structures currently lack the capability to achieve multiple, different target states with a single input actuation or require a tedious material programming step. Furthermore, the

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses a nonlinear material model with a hyperelastic incompressible Neo-Hookean membrane part and a Canham bending part. The material distribution is discretized by linear elements such that the nodal values are the design

The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the idea introduced in \cite{REZAEI2021a} for direction-dependent fracture energy and also anisotropic PF damage models based on structural tensors. The cohesive PF

This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of reference and deformed configurations as additional unknowns. Such a treatment invites compatibility of the fields with base-space (configurations of the body), so that

Fault diagnosis of rotating machinery is an important engineering problem. In recent years, fault diagnosis methods based on the Convolutional Neural Network (CNN) and Recurrent Neural Network (RNN) have been mature, but Transformer has not been widely used in the field of fault diagnosis. To address these deficiencies, a new method based on the Time Series Transformer (TST) is proposed to recognize

We develop a high accuracy power series method for solving partial differential equations with emphasis on the nonlinear Schr\"odinger equations. The accuracy and computing speed can be systematically and arbitrarily increased to orders of magnitude larger than those of other methods. Machine precision accuracy can be easily reached and sustained for long evolution times within rather short computing

The mechanical behavior of inelastic materials with microstructure is very complex and hard to grasp with heuristic, empirical constitutive models. For this purpose, multiscale, homogenization approaches are often used for performing reliable, accurate predictions of the macroscopic mechanical behavior of microstructured solids. Nevertheless, the calculation cost of such approaches is extremely high

Aortic dissection progresses via delamination of the medial layer of the wall. Notwithstanding the complexity of this process, insight has been gleaned by studying in vitro and in silico the progression of dissection driven by quasi-static pressurization of the intramural space by fluid injection, which demonstrates that the differential propensity of dissection can be affected by spatial distributions

In this article, continuous Galerkin finite elements are applied to perform full waveform inversion (FWI) for seismic velocity model building. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process

The optimization of porous infill structures via local volume constraints has become a popular approach in topology optimization. In some design settings, however, the iterative optimization process converges only slowly, or not at all even after several hundreds or thousands of iterations. This leads to regions in which a distinct binary design is difficult to achieve. Interpreting intermediate density

We summarize recent results and ongoing activities in mathematical algorithms and computer science methods related to proton computed tomography (pCT) and intensity-modulated particle therapy (IMPT) treatment planning. Proton therapy necessitates a high level of delivery accuracy to exploit the selective targeting imparted by the Bragg peak. For this purpose, pCT utilizes the proton beam itself to

Most deep-learning frameworks for understanding biological swarms are designed to fit perceptive models of group behavior to individual-level data (e.g., spatial coordinates of identified features of individuals) that have been separately gathered from video observations. Despite considerable advances in automated tracking, these methods are still very expensive or unreliable when tracking large numbers

An adaptive interpolation scheme is proposed to accurately calculate the wideband responses in electromagnetic simulations. In the proposed scheme, the sampling points are first carefully divided into several groups based on their responses to avoid the Runge phenomenon and the error fluctuations, and then different interpolation strategies are used to calculate the responses in the whole frequency

In this work we present a new physics-informed machine learning model that can be used to analyze kinematic data from an instrumented mouthguard and detect impacts to the head. Monitoring player impacts is vitally important to understanding and protecting from injuries like concussion. Typically, to analyze this data, a combination of video analysis and sensor data is used to ascertain the recorded

Efficient frequency-domain Full Waveform Inversion (FWI) of long-offset/wide-azimuth node data can be designed with a few discrete frequencies. However, 3D frequency-domain seismic modeling remains challenging since it requires solving a large and sparse linear indefinite system per frequency. When such systems are solved with direct methods or hybrid direct/iterative solvers, based upon domain decomposition

Arterial blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the design. Consequently, any reliable model of such physical processes must consider the coupling of fluids and solids. However,

This paper provides an extended level set (X-LS) based topology optimiza- tion method for multi material design. In the proposed method, each zero level set of a level set function {\phi}ij represents the boundary between materials i and j. Each increase or decrease of {\phi}ij corresponds to a material change between the two materials. This approach reduces the dependence of the initial configuration

Crystal Structure Prediction (CSP) aims to discover solid crystalline materials by optimizing periodic arrangements of atoms, ions or molecules. CSP takes weeks of supercomputer time because of slow energy minimizations for millions of simulated crystals. The lattice energy is a key physical property, which determines thermodynamic stability of a crystal but has no simple analytic expression. Past

Electromyography (EMG) refers to a biomedical signal indicating neuromuscular activity and muscle morphology. Experts accurately diagnose neuromuscular disorders using this time series. Modern data analysis techniques have recently led to introducing novel approaches for mapping time series data to graphs and complex networks with applications in diverse fields, including medicine. The resulting networks

This paper reports a reduced-order modeling framework of bladed disks on a rotating shaft to simulate the vibration signature of faults like cracks in different components aiming towards simulated data-driven machine learning. We have employed lumped and one-dimensional analytical models of the subcomponents for better insight into the complex dynamic response. The framework seeks to address some of

The so-called Locally Resonant Acoustic Metamaterials (LRAM) are considered for the design of specifically engineered devices capable of stopping waves from propagating in certain frequency regions (bandgaps), this making them applicable for acoustic insulation purposes. This fact has inspired the design of a new kind of lightweight acoustic insulation panels with the ability to attenuate noise sources

This paper proposes a level set-based topology optimization method for designing acoustic structures with viscous and thermal boundary layers in perspective. It is known that acoustic waves propagating in a narrow channel are damped by viscous and thermal boundary layers. To estimate these viscothermal effects, we first introduce a sequential linearized Navier-Stokes model based on three weakly coupled

The aerodynamic optimization process of cars requires multiple iterations between aerodynamicists and stylists. Response Surface Modeling and Reduced-Order Modeling are commonly used to eliminate the overhead due to Computational Fluid Dynamics, leading to faster iterations. However, a primary drawback of these models is that they can work only on the parametrized geometric features they were trained

Solution of Ordinary Differential Equation (ODE) model of dynamical system may not agree with its observed values. Often this discrepancy can be attributed to unmodeled forcings in the evolution rule of the dynamical system. In this article, an approach for data-based model improvement is described which exploits the geometric constraints imposed by the system observations to estimate these unmodeled

Artificial synthesis of DNA molecules is an essential part of the study of biological mechanisms. The design of a synthetic DNA molecule usually involves many objectives. One of the important objectives is to eliminate short sequence patterns that correspond to binding sites of restriction enzymes or transcription factors. While many design tools address this problem, no adequate formal solution exists

This paper extends the nonsmooth Relaxed Variational Approach (RVA) to topology optimization, proposed by the authors in a preceding work, to the solution of thermal optimization problems. First, the RVA topology optimization method is briefly discussed and, then, it is applied to a set of representative problems in which the thermal compliance, the deviation of the heat flux from a given field and

The work provides an exhaustive comparison of some representative families of topology optimization methods for 3D structural optimization, such as the Solid Isotropic Material with Penalization (SIMP), the Level-set, the Bidirectional Evolutionary Structural Optimization (BESO), and the Variational Topology Optimization (VARTOP) methods. The main differences and similarities of these approaches are

Artificial Intelligence (AI)-driven material design has been attracting great attentions as a groundbreaking technology across a wide spectrum of industries. Molecular design is particularly important owing to its broad application domains and boundless creativity attributed to progresses in generative models. The recent maturity of molecular generative models has stimulated expectations for practical

Metal additive manufacturing (AM) processes often fabricate a near-net shape that includes the as-designed part as well as the sacrificial support structures that need to be machined away by subtractive manufacturing (SM), for instance multi-axis machining. Thus, although AM is capable of generating highly complex parts, the limitations of SM due to possible collision between the milling tool and the

The aortic vessel tree is composed of the aorta and its branching arteries, and plays a key role in supplying the whole body with blood. Aortic diseases, like aneurysms or dissections, can lead to an aortic rupture, whose treatment with open surgery is highly risky. Therefore, patients commonly undergo drug treatment under constant monitoring, which requires regular inspections of the vessels through

We propose an end-to-end pipeline to robustly generate high-quality, high-order and coarse quadrilateral meshes on CAD models. This kind of mesh enables the use of high-order analysis techniques such as high-order finite element methods or isogeometric analysis. An initial unstructured mesh is generated; this mesh contains a low number of irregular vertices but these are not necessarily aligned, causing

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed characteristic function field as a topological design variable, (c) the consistent derivation of a relaxed topological derivative whose determination is simple, general

We describe three independent implementations of a new agent-based model (ABM) that simulates a contemporary sports-betting exchange, such as those offered commercially by companies including Betfair, Smarkets, and Betdaq. The motivation for constructing this ABM, which is known as the Bristol Betting Exchange (BBE), is so that it can serve as a synthetic data generator, producing large volumes of

Partition of unity methods (PUM) are of domain decomposition type and provide the opportunity for multiscale and multiphysics numerical modeling. Different physical models can exist within a PUM scheme for handling problems with zones of linear elasticity and zones where fractures occur. Here, the peridynamic (PD) model is used in regions of fracture and smooth PUM is used in the surrounding linear

An efficient and momentum conserving algorithm for enforcing contact between solid bodies is proposed. Previous advances in the material point method (MPM) led to a fast and simple, but potentially momentum violating, strategy for enforcing contact. This was achieved through a combination of velocity transfers between background and foreground grids, and a background grid velocity field update. We

To overcome many-query optimization, control, or uncertainty quantification work loads in reliable gas and energy network operations, model order reduction is the mathematical technology of choice. To this end, we enhance the model, solver and reductor components of the "morgen" platform, introduced in Himpe et al [J.~Math.~Ind. 11:13, 2021], and conclude with a mathematically, numerically and computationally

The support structure is required to successfully create structural parts in the powder bed fusion process of additive manufacturing. In this study, we present the topology optimization of the support structure that improves heat dissipation in the building process. First, we construct a numerical method that obtains the temperature field in the building process represented by the transient heat conduction

The Finite Volume Method in Computational Fluid Dynamics to numerically model a fluid flow problem involves the process of formulating the numerical flux at the faces of the control volume. This process is important in deciding the resolution of the numerical solution, thus its quality. In the current work, the performance of different flux construction methods when solving the one-dimensional Euler