Publication Server of Zuse Institute Berlin (ZIB)
Not a member yet
6648 research outputs found
Sort by
Machine learning estimation of reaction energy barriers
No full textWe describe a machine learning approach to approximate reaction energy barriers (E), requiring as input only estimates of geometry and energies of reactants and products. Using the dataset of Grambow, Pattanaik, and Green [Sci. Data 7 (1 3 7) (2020)] for reactions involving seven or fewer non-hydrogen atoms, 300 reaction features are computed, and an estimate of E is obtained by fitting a Kernel Ridge Regression (KRR) model with Laplacian kernel to a subset of Density Functional Theory reaction barriers. Our main interest is small energy barriers with the goal of modeling reactions in the interstellar medium and circumstellar envelope. We omitted reactions with E > 40 kcal mol−1 to obtain a subset of 5,276 reactions for 5-fold cross-validation. For this set, the KRR model predicts E with a mean absolute error of 4.13 kcal mol−1 and a root-mean square error of 6.02 kcal mol−1
AI-guided pipeline for protein-protein interaction drug discovery identifies a SARS-CoV-2 inhibitor
No full textEnabling research through the SCIP optimization suite 8.0
No full textThe SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. The focus of this article is on the role of the SCIP Optimization Suite in supporting research. SCIP’s main design principles are discussed, followed by a presentation of the latest performance improvements and developments in version 8.0, which serve both as examples of SCIP’s application as a research tool and as a platform for further developments. Furthermore, this article gives an overview of interfaces to other programming and modeling languages, new features that expand the possibilities for user interaction with the framework, and the latest developments in several extensions built upon SCIP
Flexible Differentiable Optimization via Model Transformations
No full textWe introduce DiffOpt.jl, a Julia library to differentiate through the solution of optimization problems with respect to arbitrary parameters present in the objective and/or constraints. The library builds upon MathOptInterface, thus leveraging the rich ecosystem of solvers and composing well with modeling languages like JuMP. DiffOpt offers both forward and reverse differentiation modes, enabling multiple use cases from hyperparameter optimization to backpropagation and sensitivity analysis, bridging constrained optimization with end-to-end differentiable programming. DiffOpt is built on two known rules for differentiating quadratic programming and conic programming standard forms. However, thanks to its ability to differentiate through model transformations, the user is not limited to these forms and can differentiate with respect to the parameters of any model that can be reformulated into these standard forms. This notably includes programs mixing affine conic constraints and convex quadratic constraints or objective function
Error Bounds for Discrete-Continuous Free Flight Trajectory Optimization
No full textFlight planning, the computation of optimal routes in view of flight time and fuel consumption under given weather conditions, is traditionally done by finding globally shortest paths in a predefined airway network. Free flight trajectories, not restricted to a network, have the potential to reduce the costs significantly, and can be computed using locally convergent continuous optimal control methods.
Hybrid methods that start with a discrete global search and refine with a fast continuous local optimization combine the best properties of both approaches, but rely on a good switchover, which requires error estimates for discrete paths relative to continuous trajectories.
Based on vertex density and local complete connectivity, we derive localized and a priori bounds for the flight time of discrete paths relative to the optimal continuous trajectory, and illustrate their properties on a set of benchmark problems. It turns out that localization improves the error bound by four orders of magnitude, but still leaves ample opportunities for tighter bounds using a posteriori error estimators
Crossing of the branch cut: the topological origin of a universal 2π-phase retardation in non-Hermitian metasurfaces
No full textFully Computer-assisted Proofs in Extremal Combinatorics
No full textWe present a fully computer-assisted proof system for solving a particular family of problems in Extremal Combinatorics. Existing techniques using Flag Algebras have proven powerful in the past, but have so far lacked a computational counterpart to derive matching constructive bounds. We demonstrate that common search heuristics are capable of finding constructions far beyond the reach of human intuition. Additionally, the most obvious downside of such heuristics, namely a missing guarantee of global optimality, can often be fully eliminated in this case through lower bounds and stability results coming from the Flag Algebra approach.
To illustrate the potential of this approach, we study two related and well-known problems in Extremal Graph Theory that go back to questions of Erdős from the 60s.
Most notably, we present the first major improvement in the upper bound of the Ramsey multiplicity of the complete graph on 4 vertices in 25 years, precisely determine the first off-diagonal Ramsey multiplicity number, and settle the minimum number of independent sets of size four in graphs with clique number strictly less than five
Coarse Grained MD Simulations of Opioid interactions with the µ-opioid receptor and the surrounding lipid membrane
No full textIn our previous studies, a new opioid (NFEPP) was developed to only selectively bind to the -opoid receptor (MOR) in inflamed tissue and thus avoid the severe side effects of fentanyl. We know that NFEPP has a reduced binding affinity to MOR in healthy tissue. Inspired by the modelling and simulations performed by Sutcliffe et al., we present our own results of coarse-grained molecular dynamics simulations of fentanyl and NFEPP with regards to their interaction with the -opioid receptor embedded within the lipid cell membrane. For technical reasons, we have slightly modified Sutcliffe’s parametrisation of opioids. The pH-dependent opioid simulations are of interest because while fentanyl is protonated at the physiological pH, NFEPP is deprotonated due to its lower pKa value than that of fentanyl. Here, we analyse for the first time whether pH changes have an effect on the dynamical behaviour of NFEPP when it is inside the cell membrane. Besides these changes, our analysis shows a possible alternative interaction of NFEPP at pH 7.4 outside the binding region of the MOR. The interaction potential of NFEPP with MOR is also depicted by analysing the provided statistical molecular dynamics simulations with the aid of an eigenvector analysis of a transition rate matrix. In our modelling, we see differences in the XY-diffusion profiles of NFEPP compared with fentanyl in the cell membrane
Interpolating between BSDEs and PINNs: deep learning for elliptic and parabolic boundary value problems
No full textSolving high-dimensional partial differential equations is a recurrent challenge in economics, science and engineering. In recent years, a great number of computational approaches have been developed,
most of them relying on a combination of Monte Carlo sampling and deep learning based approximation. For elliptic and parabolic problems, existing methods can broadly be classified into those resting on reformulations in terms of backward stochastic differential equations (BSDEs) and those aiming to minimize a regression-type L2-error (physics-informed neural networks, PINNs). In this paper, we review the literature and suggest a methodology based on the novel diffusion loss that interpolates between BSDEs and PINNs. Our contribution opens the door towards a unified understanding of numerical approaches for high-dimensional PDEs, as well as for implementations that combine the strengths of BSDEs and PINNs. The diffusion loss furthermore bears close similarities to (least squares) temporal difference objectives found in reinforcement learning. We also discuss eigenvalue problems and perform extensive numerical studies, including calculations of the
ground state for nonlinear Schr ¨odinger operators and committor functions relevant in molecular dynamics