Scalable Objective-Driven Batch Sampling in Simulation-Based Design for Models With Heteroscedastic Noise

2020 ◽  
Author(s):  
Anton van Beek ◽  
Umar Farooq Ghumman ◽  
Joydeep Munshi ◽  
Siyu Tao ◽  
TeYu Chien ◽  
...  
Keyword(s):  
Stochastic Simulation ◽  
Adaptive Sampling ◽  
Numerical Test ◽  
Computational Cost ◽  
Simulation Models ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Sampling Scheme ◽  
Sampling Location ◽  
Sampling Locations

Abstract Objective-driven adaptive sampling is a widely used tool for the optimization of deterministic black-box functions. However, the optimization of stochastic simulation models as found in the engineering, biological, and social sciences is still an elusive task. In this work, we propose a scalable adaptive batch sampling scheme for the optimization of stochastic simulation models with input-dependent noise. The developed algorithm has two primary advantages: (i) by recommending sampling batches, the designer can benefit from parallel computing capabilities, and (ii) by replicating of previously observed sampling locations the method can be scaled to higher-dimensional and more noisy functions. Replication improves numerical tractability as the computational cost of Bayesian optimization methods is known to grow cubicly with the number of unique sampling locations. Deciding when to replicate and when to explore depends on what alternative minimizes the posterior prediction accuracy at and around the spatial locations expected to contain the global optimum. The algorithm explores a new sampling location to reduce the interpolation uncertainty and replicates to improve the accuracy of the mean prediction at a single sampling location. Through the application of the proposed sampling scheme to two numerical test functions and one real engineering problem, we show that we can reliably and efficiently find the global optimum of stochastic simulation models with input-dependent noise.

Scalable Adaptive Batch Sampling in Simulation-Based Design With Heteroscedastic Noise

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Anton van Beek ◽  
Umar Farooq Ghumman ◽  
Joydeep Munshi ◽  
Siyu Tao ◽  
TeYu Chien ◽  
...  
Keyword(s):  
Adaptive Sampling ◽  
Order Approximation ◽  
Numerical Test ◽  
Computational Cost ◽  
Superior Performance ◽  
Sampling Scheme ◽  
Test Functions ◽  
Zeroth Order ◽  
Sampling Locations ◽  
Spatially Varying

Abstract In this study, we propose a scalable batch sampling scheme for optimization of simulation models with spatially varying noise. The proposed scheme has two primary advantages: (i) reduced simulation cost by recommending batches of samples at carefully selected spatial locations and (ii) improved scalability by actively considering replicating at previously observed sampling locations. Replication improves the scalability of the proposed sampling scheme as the computational cost of adaptive sampling schemes grow cubicly with the number of unique sampling locations. Our main consideration for the allocation of computational resources is the minimization of the uncertainty in the optimal design. We analytically derive the relationship between the “exploration versus replication decision” and the posterior variance of the spatial random process used to approximate the simulation model’s mean response. Leveraging this reformulation in a novel objective-driven adaptive sampling scheme, we show that we can identify batches of samples that minimize the prediction uncertainty only in the regions of the design space expected to contain the global optimum. Finally, the proposed sampling scheme adopts a modified preposterior analysis that uses a zeroth-order interpolation of the spatially varying simulation noise to identify sampling batches. Through the optimization of three numerical test functions and one engineering problem, we demonstrate (i) the efficacy and of the proposed sampling scheme to deal with a wide array of stochastic functions, (ii) the superior performance of the proposed method on all test functions compared to existing methods, (iii) the empirical validity of using a zeroth-order approximation for the allocation of sampling batches, and (iv) its applicability to molecular dynamics simulations by optimizing the performance of an organic photovoltaic cell as a function of its processing settings.

Applying Bayesian Optimization for Calibration of Transportation Simulation Models

2020 ◽  
Vol 2674 (10) ◽  
pp. 215-228
Author(s):  
Di Sha ◽  
Kaan Ozbay ◽  
Yue Ding
Keyword(s):  
Simulation Model ◽  
Simulation Models ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Local Optimum ◽  
Computationally Efficient ◽  
Actual System ◽  
Transportation Simulation ◽  
Calibration Accuracy ◽  
Comparative Results

The parameters of a transportation simulation model need to pass through a careful calibration process to ensure that the model’s output is as close as possible to the actual system. Owing to the computationally expensive and black-box nature of a simulation model, there is a need for robust and efficient calibration algorithms. This paper proposes a Bayesian optimization framework for the high-dimensional calibration problem of transportation simulation models. Bayesian optimization uses acquisition functions to determine more promising values for future evaluation, instead of relying on local gradient approximations. It guarantees convergence to the global optimum with a reduced number of evaluations, therefore is very computationally efficient. The proposed algorithm is applied to the calibration of a simulation network coded in simulation of urban mobility (SUMO), an open-source microscopic transportation simulation platform, and compared with a well-known method named simultaneous perturbation stochastic approximation (SPSA). To assess the calibration accuracy, speed distributions obtained from the two models calibrated using these two different methods are compared with the observation. For both the Bayesian optimization and SPSA results, the simulated and observed distributions are validated to be from the same distribution at a 95% confidence level for multiple sensor locations. Thus, the calibration accuracy of the two approaches are both acceptable for a stochastic transportation simulation model. However, Bayesian optimization shows a better convergence and a higher computational efficiency than SPSA. In addition, the comparative results of multiple implementations validate its robustness for a noisy objective function, unlike SPSA which may sometimes get stuck in a local optimum and fail to converge in a global solution.

Multi-Model Bayesian Optimization for Simulation-Based Design (DETC2020-22651)

2021 ◽  
pp. 1-39
Author(s):  
Siyu Tao ◽  
Anton van Beek ◽  
Daniel Apley ◽  
Wei Chen
Keyword(s):  
Simulation Models ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
System Response ◽  
Engineering Systems ◽  
Simulation Based Design ◽  
Simulation Based ◽  
Need To Evaluate ◽  
Complex Engineering ◽  
Component Models

Abstract We enhance the Bayesian optimization (BO) approach for simulation-based design of engineering systems consisting of multiple interconnected expensive simulation models. The goal is to find the global optimum design with minimal model evaluation costs. A commonly used approach is to treat the whole system as a single expensive model and apply an existing BO algorithm. This approach is inefficient due to the need to evaluate all the component models in each iteration. We propose a multi-model BO approach that dynamically and selectively evaluates one component model per iteration based on the uncertainty quantification of linked emulators (metamodels) and the knowledge gradient of system response as the acquisition function. Building on our basic formulation, we further solve problems with constraints and feedback couplings that often occur in real complex engineering design by penalizing the objective emulator and reformulating the original problem into a decoupled one. The superior efficiency of our approach is demonstrated through solving two analytical problems and the design optimization of a multidisciplinary electronic packaging system.

Nanosecond Photodynamics Simulations of a Cis-Trans Isomerization Are Enabled by Machine Learning

2020 ◽  
Author(s):  
Jingbai Li ◽  
Patrick Reiser ◽  
André Eberhard ◽  
Pascal Friederich ◽  
Steven Lopez
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Excited State ◽  
Adaptive Sampling ◽  
Computational Cost ◽  
Ground Truth ◽  
Absolute Error ◽  
Photochemical Reactions ◽  
Computational Techniques ◽  
Full Potential

<p>Photochemical reactions are being increasingly used to construct complex molecular architectures with mild and straightforward reaction conditions. Computational techniques are increasingly important to understand the reactivities and chemoselectivities of photochemical isomerization reactions because they offer molecular bonding information along the excited-state(s) of photodynamics. These photodynamics simulations are resource-intensive and are typically limited to 1–10 picoseconds and 1,000 trajectories due to high computational cost. Most organic photochemical reactions have excited-state lifetimes exceeding 1 picosecond, which places them outside possible computational studies. Westermeyr <i>et al.</i> demonstrated that a machine learning approach could significantly lengthen photodynamics simulation times for a model system, methylenimmonium cation (CH<sub>2</sub>NH<sub>2</sub><sup>+</sup>).</p><p>We have developed a Python-based code, Python Rapid Artificial Intelligence <i>Ab Initio</i> Molecular Dynamics (PyRAI<sup>2</sup>MD), to accomplish the unprecedented 10 ns <i>cis-trans</i> photodynamics of <i>trans</i>-hexafluoro-2-butene (CF<sub>3</sub>–CH=CH–CF<sub>3</sub>) in 3.5 days. The same simulation would take approximately 58 years with ground-truth multiconfigurational dynamics. We proposed an innovative scheme combining Wigner sampling, geometrical interpolations, and short-time quantum chemical trajectories to effectively sample the initial data, facilitating the adaptive sampling to generate an informative and data-efficient training set with 6,232 data points. Our neural networks achieved chemical accuracy (mean absolute error of 0.032 eV). Our 4,814 trajectories reproduced the S<sub>1</sub> half-life (60.5 fs), the photochemical product ratio (<i>trans</i>: <i>cis</i> = 2.3: 1), and autonomously discovered a pathway towards a carbene. The neural networks have also shown the capability of generalizing the full potential energy surface with chemically incomplete data (<i>trans</i> → <i>cis</i> but not <i>cis</i> → <i>trans</i> pathways) that may offer future automated photochemical reaction discoveries.</p>

scholarly journals Global optimization based on active preference learning with radial basis functions

2020 ◽  
Author(s):  
Alberto Bemporad ◽  
Dario Piga
Keyword(s):  
Global Optimization ◽  
Objective Function ◽  
Decision Maker ◽  
Optimization Problems ◽  
Global Optimum ◽  
Bayesian Optimization ◽  
Preference Learning ◽  
Global Optimizer ◽  
Radial Basis ◽  
Decision Vector

AbstractThis paper proposes a method for solving optimization problems in which the decision-maker cannot evaluate the objective function, but rather can only express a preference such as “this is better than that” between two candidate decision vectors. The algorithm described in this paper aims at reaching the global optimizer by iteratively proposing the decision maker a new comparison to make, based on actively learning a surrogate of the latent (unknown and perhaps unquantifiable) objective function from past sampled decision vectors and pairwise preferences. A radial-basis function surrogate is fit via linear or quadratic programming, satisfying if possible the preferences expressed by the decision maker on existing samples. The surrogate is used to propose a new sample of the decision vector for comparison with the current best candidate based on two possible criteria: minimize a combination of the surrogate and an inverse weighting distance function to balance between exploitation of the surrogate and exploration of the decision space, or maximize a function related to the probability that the new candidate will be preferred. Compared to active preference learning based on Bayesian optimization, we show that our approach is competitive in that, within the same number of comparisons, it usually approaches the global optimum more closely and is computationally lighter. Applications of the proposed algorithm to solve a set of benchmark global optimization problems, for multi-objective optimization, and for optimal tuning of a cost-sensitive neural network classifier for object recognition from images are described in the paper. MATLAB and a Python implementations of the algorithms described in the paper are available at http://cse.lab.imtlucca.it/~bemporad/glis.

Adaptive sampling of potential-field data: A direct approach to compressive inversion

Geophysics ◽  
2014 ◽  
Vol 79 (1) ◽  
pp. IM1-IM9 ◽  
Author(s):  
Nathan Leon Foks ◽  
Richard Krahenbuhl ◽  
Yaoguo Li
Keyword(s):  
Potential Field ◽  
Adaptive Sampling ◽  
Field Data ◽  
Computational Cost ◽  
Large Field ◽  
Magnetic Data ◽  
Data Sampling ◽  
Data Types ◽  
Data Set ◽  
Potential Field Data

Compressive inversion uses computational algorithms that decrease the time and storage needs of a traditional inverse problem. Most compression approaches focus on the model domain, and very few, other than traditional downsampling focus on the data domain for potential-field applications. To further the compression in the data domain, a direct and practical approach to the adaptive downsampling of potential-field data for large inversion problems has been developed. The approach is formulated to significantly reduce the quantity of data in relatively smooth or quiet regions of the data set, while preserving the signal anomalies that contain the relevant target information. Two major benefits arise from this form of compressive inversion. First, because the approach compresses the problem in the data domain, it can be applied immediately without the addition of, or modification to, existing inversion software. Second, as most industry software use some form of model or sensitivity compression, the addition of this adaptive data sampling creates a complete compressive inversion methodology whereby the reduction of computational cost is achieved simultaneously in the model and data domains. We applied the method to a synthetic magnetic data set and two large field magnetic data sets; however, the method is also applicable to other data types. Our results showed that the relevant model information is maintained after inversion despite using 1%–5% of the data.

scholarly journals STOCHASTIC OPTIMIZATION OF HEURISTIC METHOD RULE TO DETERMINE ASSET ALLOCATION TO RETIREMENT PORTFOLIO / STOCHASTINIS EURISTINIO METODO TAISYKLĖS PENSIJOS PORTFELIO SUDĖČIAI NUSTATYTI OPTIMIZAVIMAS

2011 ◽  
Vol 12 (1) ◽  
pp. 92-98
Author(s):  
Aušra Klimavičienė
Keyword(s):  
Stochastic Optimization ◽  
Stochastic Simulation ◽  
Asset Allocation ◽  
Heuristic Method ◽  
Simulation Models ◽  
Optimization Techniques ◽  
Human Lifespan ◽  
Stochastic Returns ◽  
Dynamic Stochastic ◽  
Population Mortality

The article examines the problem of determining asset allocation to sustainable retirement portfolio. The article attempts to apply heuristic method – 100 minus age in stocks rule – to determine asset allocation to sustainable retirement portfolio. Using dynamic stochastic simulation and stochastic optimization techniques the optimization of heuristic method rule is presented and the optimal alternative to „100“ is found. Seeking to reflect the stochastic nature of stock and bond returns and the human lifespan, the dynamic stochastic simulation models incorporate both the stochastic returns and the probability of living another year based on Lithuania‘s population mortality tables. The article presents the new method – adjusted heuristic method – to be used to determine asset allocation to retirement portfolio and highlights its advantages.

scholarly journals Numerical studies of higher order tau-leaping methods

2021 ◽  
Author(s):  
Anuj Dhoj Thapa
Keyword(s):  
Stochastic Simulation ◽  
Computational Cost ◽  
Practical Interest ◽  
Stochastic Simulation Algorithm ◽  
Simulation Method ◽  
Equation Model ◽  
Fast Reactions ◽  
Biochemical Systems ◽  
Computationally Intensive ◽  
Reacting Systems

Gillespie's algorithm, also known as the Stochastic Simulation Algorithm (SSA), is an exact simulation method for the Chemical Master Equation model of well-stirred biochemical systems. However, this method is computationally intensive when some fast reactions are present in the system. The tau-leap scheme developed by Gillespie can speed up the stochastic simulation of these biochemically reacting systems with negligible loss in accuracy. A number of tau-leaping methods were proposed, including the explicit tau-leaping and the implicit tau-leaping strategies. Nonetheless, these schemes have low order of accuracy. In this thesis, we investigate tau-leap strategies which achieve high accuracy at reduced computational cost. These strategies are tested on several biochemical systems of practical interest.

An Adaptive Sampling Scheme for Out-of-Core Simplification

2002 ◽  
Vol 21 (2) ◽  
pp. 111-118 ◽  
Author(s):  
Guangzheng Fei ◽  
Kangying Cai ◽  
Baining Guo ◽  
Enhua Wu
Keyword(s):  
Adaptive Sampling ◽  
Sampling Scheme
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