相关论文: Low-Scaling Algorithm for Nudged Elastic Band Calc…

In a task where many similar inverse problems must be solved, evaluating costly simulations is impractical. Therefore, replacing the model $y$ with a surrogate model $y_s$ that can be evaluated quickly leads to a significant speedup. The…

Saddle point search schemes are widely used to identify the transition state of different processes, like chemical reactions, surface and bulk diffusion, surface adsorption, and many more. In solid-state materials with relatively large…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

Gaussian process (GP) regression provides a strategy for accelerating saddle point searches on high-dimensional energy surfaces by reducing the number of times the energy and its derivatives with respect to atomic coordinates need to be…

Hierarchical computational methods for multiscale mechanics such as the FE$^2$ and FE-FFT methods are generally accompanied by high computational costs. Data-driven approaches are able to speed the process up significantly by enabling to…

Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate,…

The minimum energy path (MEP) describes the mechanism of reaction, and the energy barrier along the path can be used to calculate the reaction rate in thermal systems. The nudged elastic band (NEB) method is one of the most commonly used…

Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However,…

Kernel-based models such as kernel ridge regression and Gaussian processes are ubiquitous in machine learning applications for regression and optimization. It is well known that a major downside for kernel-based models is the high…

Markov chain Monte Carlo methods for exponential family models with intractable normalizing constant, such as the exchange algorithm, require simulations of the sufficient statistics at every iteration of the Markov chain, which often…

Recently, a Gaussian Process Regression - neural network (GPRNN) hybrid machine learning method was proposed, which is based on additive-kernel GPR in redundant coordinates constructed by rules [J. Phys. Chem. A 127 (2023) 7823]. The method…

We propose a nested Gaussian process (nGP) as a locally adaptive prior for Bayesian nonparametric regression. Specified through a set of stochastic differential equations (SDEs), the nGP imposes a Gaussian process prior for the function's…

We are interested in building low-dimensional surrogate models to reduce optimization costs, while having theoretical guarantees that the optimum will satisfy the constraints of the full-size model, by making conservative approximations.…

Symbolic regression is an important but challenging research topic in data mining. It can detect the underlying mathematical models. Genetic programming (GP) is one of the most popular methods for symbolic regression. However, its…

Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a…

The optimization of structural parameters, such as mass(m), stiffness(k), and damping coefficient(c), is critical for designing efficient, resilient, and stable structures. Conventional numerical approaches, including Finite Element Method…

In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a new algorithm for the convex finite-sum minimization problems. Our method integrates the traditional Nesterov's acceleration momentum with different shuffling…

Uncertainty Quantification (UQ) is essential for the reliable application of computational models in engineering and science. Among surrogate modeling techniques, Gaussian Process Regression (GPR) is particularly valuable for its…

Retinal prostheses restore vision by electrically stimulating surviving neurons, but calibrating perceptual thresholds (i.e., the minimum stimulus intensity required for perception) remains a time-intensive challenge, especially for…

Euler's elastica model has been extensively studied and applied to image processing tasks. However, due to the high nonlinearity and nonconvexity of the involved curvature term, conventional algorithms suffer from slow convergence and high…