Related papers: JAX-BEM: Gradient-Based Acoustic Shape Optimisatio…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
The co-optimization of geometry and physical parameters remains challenging in transient multiphysics systems involving moving boundaries, nonlinear material response, phase transitions, and competing objectives. Existing methods often…
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
The rapid rise of scientific machine learning (SciML) has expanded the role of differentiable modeling, surrogate modeling, and data-driven constitutive laws in large-scale simulation. The JAX framework provides an attractive environment…
This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…
The versatile Arbitrary-DERivative (ADER) scheme is cast in a multilevel framework (ML-ADER) for fast solution of system of linear hyperbolic partial differential equations. The solution is cycled through spatial operators of varying…
Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype…
Optimization benchmarks play a fundamental role in assessing algorithm performance; however, existing artificial benchmarks often fail to capture the diversity and irregularity of real-world problem structures, while benchmarks derived from…
Quick simulations for iterative evaluations of multi-design variables and boundary conditions are essential to find the optimal acoustic conditions in building design. We propose to use the reduced basis method (RBM) for realistic room…
In this paper we develop a class of efficient Galerkin boundary element methods for the solution of two-dimensional exterior single-scattering problems. Our approach is based upon construction of Galerkin approximation spaces confined to…
A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…
High-fidelity simulations, such as computational fluid dynamics and finite element analysis, are essential for modeling complex engineering systems but are often prohibitively expensive for tasks including parametric studies, optimization,…
The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…
To leverage data and computation capabilities of mobile devices, machine learning algorithms are deployed at the network edge for training artificial intelligence (AI) models, resulting in the new paradigm of edge learning. In this paper,…
Although freeform devices with complex internal structures promise drastic increases in performance, the discreteness of the set of available materials presents challenges for gradient-based optimization necessary for the efficient…
We introduce a framework for Bayesian experimental design (BED) with implicit models, where the data-generating distribution is intractable but sampling from it is still possible. In order to find optimal experimental designs for such…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…
We are interested in time-harmonic acoustic scattering by an impenetrable obstacle in a medium where the wavenumber is constant in an exterior unbounded subdomain and is possibly heterogeneous in a bounded subdomain. The associated…
In this work, possibility of simulating biological organs in realtime using the Boundary Element Method (BEM) is investigated. Biological organs are assumed to follow linear elastostatic material behavior, and constant boundary element is…