24 papers · ranked by Valyu relevance
B. Sengupta, K.J. Friston, W.D. Penny
Data assimilation is a fundamental issue that arises across many scales in neuroscience - ranging from the study of single neurons using single electrode recordings to the interaction of thousands of neurons using fMRI. Data assimilation involves inverting a generative model that can not only explain observed data but…
Paolo Luchini, Alessandro Bottaro
| 1 Historical remarks | | 2 | | --- | --- | --- | | 2 | The simplest example: transpose of a matrix | 2 | | 3 | What are adjoints used for? | 4 | | 4 | Adjoint of a system of linear algebraic equations | 4 | | 5 | Entering dynamics: the adjoint of a discrete-time dynamical system . | 5 | | 6 From discrete to…
Calum S. Skene, Keaton J. Burns
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 differentiation to symbolic graph representations of PDEs, efficiently constructing…
Mingyu Park, Haejun Chung, Kyung-Young Jung
Title: Summary We propose a time-domain adjoint optimization method for achromatic metalens design, achieving high efficiency and near-uniform spectral response. Unlike frequency-domain approaches, which require simulations for each sampled frequency, our method evaluates the entire frequency band continuously with…
Mohamed Hayek, Jeremy T. White, Katherine H. Markovich, Joseph D. Hughes + 1 more
Adjoint sensitivity analysis provides an efficient alternative to direct methods when evaluating the influence of many uncertain parameters on a limited number of performance measures in hydrologic and hydrogeologic models. However, most adjoint implementations are “intrusive”, requiring extensive modifications of the…
Steven M. Kast
We begin with a discussion of adjoint vectors in the context of steady-state partial differential equations. We first derive adjoints in both a discrete and continuous context, then show how they can be used to compute output error estimates and perform output-based mesh adaptation. For additional information, see…
Stefan Oberpeilsteiner, Thomas Lauss, Wolfgang Steiner, Karin Nachbagauer
'Karin Nachbagauer'] The adjoint method shows an efficient way to incorporate inverse dynamics to engineering multibody applications, as, e.g., parameter identification. In case of the identification of parameters in oscillating multibody systems, a combination of Fourier analysis and the adjoint method is an obvious…
Hongyuan Jia, Hideki Kikumoto
This study developed a backward-Eulerian footprint modelling method based on an adjoint equation for atmospheric boundary-layer flows. In the proposed method, the concentration footprint can be obtained directly by numerical simulation with the adjoint equation, and the flux footprints can be estimated using the…
Paul Stapor, Fabian Fröehlich, Jan Hasenauer
Parameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with…
Gabriel Peery, Toni M. West, Sanjana S. Chemuturi, Jodie H. Pham + 2 more
We have recently documented significant compressible behaviors in hydrogels implemented in 3D traction force microscopy (TFM). Therefore, here we have developed a new computational pipeline that accounts for this observation. Additionally, the new method accurately recovers large ranges and spatial heterogeneity of…
Thomas Lauß, Stefan Oberpeilsteiner, Wolfgang Steiner, Karin Nachbagauer
'Karin Nachbagauer'] The adjoint method is an elegant approach for the computation of the gradient of a cost function to identify a set of parameters. An additional set of differential equations has to be solved to compute the adjoint variables, which are further used for the gradient computation. However, the accuracy…
Polina Lakrisenko, Paul Stapor, Stephan Grein, Łukasz Paszkowski + 5 more
Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However…
William C. Tyson, Christopher J. Roy
Adjoint methods have gained popularity in recent years for driving adaptation procedures which aim to reduce error in solution functionals. While adjoint methods have been proven effective for functional-based adaptation, the practical implementation of an adjoint method can be quite burdensome since code developers…
Leonard Schmiester, Yannik Schälte, Fabian Fröhlich, Jan Hasenauer + 1 more
Mechanistic models of biochemical reaction networks facilitate the quantitative understanding of biological processes and the integration of heterogeneous datasets. However, some biological processes require the consideration of comprehensive reaction networks and therefore large-scale models. Parameter estimation for…
Fabian Fröhlich, Barbara Kaltenbacher, Fabian J. Theis, Jan Hasenauer
Mechanistic mathematical modeling of biochemical reaction networks using ordinary differential equation (ODE) models has improved our understanding of small-and medium-scale biological processes. While the same should in principle hold for large-and genome-scale processes, the computational methods for the analysis of…
S. Wagner, F. Lucka, J. Vorwerk, C.S. Herrmann + 3 more
To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely…
Authors not listed
We comment on the work on convex regions of the potential energy surface (PES) of a molecule by M. Gunde; A. Jay; M. Poberˇznik; N. Salles; N. Richard; G. Landa; N. Mousseau; L. Martin-Samos and A. Hemeryck [J. Chem. Phys. 160, 232501 (2024)]. In contrast to the activation-relaxation technique nouveau (ARTn), in the…
Brahim Benhammouda
The purpose of this paper is to propose a novel technique to solve the Euler-Lagrange equations efficiently. This technique applies the Adomian decomposition method (ADM) directly to these equations. The great advantage of our technique is that it neither applies complex transformations to the equations nor uses…
Authors not listed
Quantum computing offers a promising platform to address the computational challenges inherent in quantum chemistry, and particularly in valence bond (VB) methods, which are chemically appealing but suffer from high computational cost due to the use of nonorthogonal orbitals. While various fermionic-to-spin mappings…
M. K. Mak, Chun Sing Leung, Tiberiu Harko
> Abstract. The Adomian Decomposition Method (ADM) is a very effective approach for solving broad classes of nonlinear partial and ordinary differential equations, with important applications in different fields of applied mathematics, engineering, physics and biology. It is the goal of the present paper to provide a…
Nicolai Machholdt Høyer, Ove Christiansen
We present a new quasi-direct quantum molecular dynamics computational method which offer a compromise between quantum dynamics using a pre-computed potential energy surface (PES) and fully direct quantum dynamics. This method is termed the time-dependent adaptive density-guided approach (TD-ADGA) and is a method for…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Hsing-Ta Chen, Junhan Chen, Vale Cofer-Shabica, Zeyu Zhou + 4 more
We present an efficient set of methods for propagating excited-state dynamics involving a large number of electronic states based on a CIS electronic state overlap scheme. Specifically, (i) following Head-Gordon et al, we implement an exact evaluation of the overlap of singly-excited electronic states at different…
Sharma Yamijala, M. Belen Oviedo, Bryan Wong
This review focuses on the application of Density Functional Tight Binding (DFTB) to electronic-excited states, which has attracted significant attention for extending the computationally efficient approach to the time domain. The chapter highlights the use of real-time time-dependent-DFTB to probe the electron…