Related papers: Adjoint characteristic decomposition of one-dimens…
In one calculation, adjoint sensitivity analysis provides the gradient of a quantity of interest with respect to all system's parameters. Conventionally, adjoint solvers need to be implemented by differentiating computational models, which…
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the…
This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability…
Derivatives of differential equation solutions are commonly for parameter estimation, fitting neural differential equations, and as model diagnostics. However, with a litany of choices and a Cartesian product of potential methods, it can be…
Room geometry inference algorithms rely on the localization of acoustic reflectors to identify boundary surfaces of an enclosure. Rooms with highly absorptive walls or walls at large distances from the measurement setup pose challenges for…
We present a complete analytical derivation of the equations used for stationary and nonstationary wave systems regarding resonant sound transmission and reflection described by the phenomenological Coupled-Mode Theory. We calculate the…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
Designing free-form photonic devices is fundamentally challenging due to the vast number of possible geometries and the complex requirements of fabrication constraints. Traditional inverse-design approaches--whether driven by human…
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…
Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total…
The design space of dynamic multibody systems (MBSs), particularly those with flexible components, is considerably large. Consequently, having a means to efficiently explore this space and find the optimum solution within a feasible…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
One difficulty in developing numerical methods for hyperbolic systems of conservation laws is the fact that solutions often contain regions where much higher resolution is required than elsewhere in the domain, particularly since the…
We present a mechanism to explicitly couple the finite-difference discretizations of 2D acoustic and isotropic elastic wave systems that are separated by straight interfaces. Such coupled simulations allow the application of the elastic…
We use the adjoint methods to study the static Hamilton-Jacobi equations and to prove the speed of convergence for those equations. The main new ideas are to introduce adjoint equations corresponding to the formal linearizations of…
With their ability to handle an increased amount of information, multivariate and multichannel signals can be used to solve problems normally not solvable with signals obtained from a single source. One such problem is the decomposition…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
This article presents the experimental characterization of nonreciprocal elastic wave transmission in a single-mode elastic waveguide. This asymmetric system is obtained by coupling a selection layer with a conversion layer: the selection…
The implementation of the discrete adjoint method for exponential time differencing (ETD) schemes is considered. This is important for parameter estimation problems that are constrained by stiff time-dependent PDEs when the discretized PDE…
A mechanism is described to symmetrize the ultraspherical spectral method for self-adjoint problems. The resulting discretizations are symmetric and banded. An algorithm is presented for an adaptive spectral decomposition of self-adjoint…