23 papers · ranked by Valyu relevance
Philipp Hoffmann
This article provides an overview of some of the mathematical principles of Automatic Differentiation (AD). In particular, we summarise different descriptions of the Forward Mode of AD, like the matrix-vector product based approach, the idea of lifting functions to the algebra of dual numbers, the method of Taylor…
Wu Hsiung Wu, Feng Sheng Wang, Maw Shang Chang
Background Mathematical modeling has been applied to the study and analysis of complex biological systems for a long time. Some processes in biological systems, such as the gene expression and feedback control in signal transduction networks, involve a time delay. These systems are represented as delay differential…
Siva Rajesh Kasa, Vaibhav Rajan
We study two practically important cases of model based clustering using Gaussian Mixture Models: (1) when there is misspecification and (2) on high dimensional data, in the light of recent advances in Gradient Descent (GD) based optimization using Automatic Differentiation (AD). Our simulation studies show that EM has…
Samer Abdallah
Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial derivatives of the result with respect to any of its inputs, without making any…
Shaoyi Yang
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure that directly affect the stability and effectiveness of the solution. In this…
Paige Bright, Alan Edelman, Steven G. Johnson
The first time that Professor Edelman had heard about automatic differentiation (AD), it was easy for him to imagine what it was . . . but what he imagined was wrong! In his head, he thought it was straightforward symbolic differentiation applied to code—sort of like executing Mathematica or Maple, or even just…
Marius Pille, Leon Martin, Emilius Richter, Dionysios Perdikis + 2 more
Personalized brain modeling at clinically relevant scales requires integrating biophysical models with empirical neuroimaging data, yet high-dimensional parameter estimation in whole-brain network models remains computationally prohibitive. We present TVB-Optim, an open-source Python library providing a general and…
John Masse, Clara Masse, François Ollivier
We investigate the automatic differentiation of hybrid models, viz. models that may contain delays, logical tests and discontinuities or loops. We consider differentiation with respect to parameters, initial conditions or the time. We emphasize the case of a small number of derivations and iterated differentiations are…
Peter Gangl, Kevin Sturm, Michael Neunteufel, Joachim Schöberl
In this paper, we present a framework for automated shape differentiation in the finite element software NGSolve. Our approach combines the mathematical Lagrangian approach for differentiating PDE-constrained shape functions with the automated differentiation capabilities of NGSolve. The user can decide which degree of…
Atılım Güneş Baydin, Barak A. Pearlmutter
Automatic differentiation—the mechanical transformation of numeric computer programs to calculate derivatives efficiently and accurately—dates to the origin of the computer age. Reverse mode automatic differentiation both antedates and generalizes the method of backwards propagation of errors used in machine learning.…
Soeren Laue
We show that forward mode automatic differentiation and symbolic differentiation are equivalent in the sense that they both perform the same operations when computing derivatives. This is in stark contrast to the common claim that they are substantially different. The difference is often illustrated by claiming that…
Hend Dawood, Nefertiti Megahed, Nicholas Higham
Acquiring reliable knowledge amidst uncertainty is a topical issue of modern science. Interval mathematics has proved to be of central importance in coping with uncertainty and imprecision. Algorithmic differentiation, being superior to both numeric and symbolic differentiation, is nowadays one of the most celebrated…
Hamza Farooq, Yongxin Chen, Ghulam Rasool, Tryphon T. Georgiou + 1 more
Accurate characterization of the brain microstructure using diffusion MRI (dMRI) relies on optimal (i.e. information-rich) scanning protocols. Presently, without such protocols, extensive datasets are necessary to image the intricate microarchitecture of the brain by fitting complex biophysical models to the data. This…
Benjamin Lieser, Georgy Belousov, Johannes Söding
Background Most popular tools for reconstructing phylogenetic trees from multiple sequence alignments use a model of molecular evolution in which a single substitution matrix or a small set of fixed matrices are shared between all columns. Models with column-specific rate matrices can in principle be fit by automatic…
Erica C. Mitchell, Justin M. Turney, Henry F. Schaefer III
for Explicitly Correlated MP2 Authors: ['Erica\nC. Mitchell' 'Justin M. Turney' 'Henry F. Schaefer III'] Automatic differentiation (AD) offers a route to achieve arbitrary-order derivatives of challenging wave function methods without the use of analytic gradients or response theory. Currently, AD has been…
Rachel Mester, Alfonso Landeros, Chris Rackauckas, Kenneth Lange
Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to…
Xinyan Wang, Jichen Li, Lan Yang, Feiyang Chen + 5 more
In the simulation of molecular systems, the underlying force field (FF) model plays an extremely important role, determining the reliability of the simulation. However, the quality of the state-of-the-art molecular force fields is still unsatisfactory in many cases, and the FF parameterization process largely relies on…
Krishna Rijal, Pankaj Mehta
The Gillespie algorithm is commonly used to simulate and analyze complex chemical reaction networks. Here, we leverage recent breakthroughs in deep learning to develop a fully differentiable variant of the Gillespie algorithm. The differentiable Gillespie algorithm (DGA) approximates discontinuous operations in the…
Authors not listed
The modeling of chemical reactions using artificial intelligence is rapidly advancing but still heavily relies on abundant and costly experimental data. In the context of computational chemistry, we present SymChemAI, a chemically informed neural network capable of simulating the dynamic evolution of reactions from…
Authors not listed
This Perspective is focused on Permutationally invariant polynomials (PIPs). Since their introduction in 2004 and first use in developing a fully permutationally invariant potential for the highly fluxional cation CH+5 , PIPs have found widespread use in developing machine learned potentials (MLPs) for isolated…
Hiroshi Nakano, Shinnosuke Hattori, Hajime Kobayashi, Takumi Araki + 3 more
In this paper, we present a new force field (FF) parameterization method with direct matching of crystal structures and atomic charges optimization in end-to-end differentiable manner. The advancement of force field (FF) parameterization methods has been accelerated by differentiable programming. Automatic…
Kan Hatakeyama-Sato, Hiroki Ishikawa, Shinya Takaishi, Yasuhiko Igarashi + 2 more
This study proposes an automated system for synthesizing polyamic acid particles using a custom liquid-handling device and a robotic arm. Integrating cameras and a multimodal large language model facilitates continuous monitoring and documentation, enhancing objectivity in synthetic experiments, and enabling future…
Lakshani Weerarathna, Oliver Weismantel, Tanja Junkers
A fully automated robotic synthesizer for the screening of amphiphilic block copolymer nanoparticle synthesis is presented. To reach this aim, block copolymer solutions are mixed in continuous flow with water, allowing for the automated variation of overall polymer concentration, mixing ratio of the water and organic…