Related papers: Optimization of Flat to Round Transformers with Se…
The development of inverse design, where computational optimization techniques are used to design devices based on certain specifications, has led to the discovery of many compact, non-intuitive structures with superior performance. Among…
In our recent work \cite{StojnicHopBnds10} we looked at a class of random optimization problems that arise in the forms typically known as Hopfield models. We viewed two scenarios which we termed as the positive Hopfield form and the…
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of…
Many physical questions in fluid dynamics can be recast in terms of norm constrained optimisation problems; which in-turn, can be further recast as unconstrained problems on spherical manifolds. Due to the nonlinearities of the governing…
An adjoint-based shape optimization method for solid bodies subjected to both rarefied and continuum gas flows is proposed. The gas-kinetic BGK equation with the diffuse-reflection boundary condition is used to describe the multiscale gas…
A system of reduced equations is proposed for the electron motion in the strongly-radiation dominated regime for an arbitrary electromagnetic field configuration. The developed approach is used to analyze various scenarios of an electron…
A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of…
Magnetized beams beam with significant canonical angular momentum are critical to electron cooling of hadron beams such as contemplated in next-generation hadron and electron-ion colliders. The transport of magnetized electron beams over…
We present a general and automated approach for computing model gradients for PDE solvers built on sparse spectral methods, and implement this capability in the widely used open-source Dedalus framework. We apply reverse-mode automatic…
The conjugate gradient method is a widely used algorithm for the numerical solution of a system of linear equations. It is particularly attractive because it allows one to take advantage of sparse matrices and produces (in case of infinite…
Forward and inverse models are used throughout different engineering fields to predict and understand the behaviour of systems and to find parameters from a set of observations. These models use root-finding and minimisation techniques…
We present a method for stellarator coil design via gradient-based optimization of the coil-winding surface. The REGCOIL (Landreman 2017 Nucl. Fusion 57 046003) approach is used to obtain the coil shapes on the winding surface using a…
In this paper we demonstrate a new technique for deriving discrete adjoint and tangent linear models of finite element models. The technique is significantly more efficient and automatic than standard algorithmic differentiation techniques.…
Transformer models have emerged as fundamental tools across various scientific and engineering disciplines, owing to their outstanding performance in diverse applications. Despite this empirical success, the theoretical foundations of…
Momentum-based gradients are essential for optimizing advanced machine learning models, as they not only accelerate convergence but also advance optimizers to escape stationary points. While most state-of-the-art momentum techniques utilize…
We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous…
The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree--Fock equations for atoms interacting both with each other and with an external potential. Our development…
In this paper we present a topology optimization technique applicable to a broad range of flow design problems. We propose also a discrete adjoint formulation effective for a wide class of Lattice Boltzmann Methods (LBM). This adjoint…