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Surrogate-based 0-th Order Global Optimization for black-box problems. This software is comprised of active learning algorithms based on surrogate models to solve black-box optimization problems and other scientific applications. See also: https://pypi.org/project/soogo/
Many engineering applications require the simultaneous optimization of multiple conflicting objective functions. Often, these objective functions are evaluated using highly accurate computer simulations that are computationally too expensive to be evaluated hundreds or thousands of times during optimization. Thus, the goal is to find good approximations of the Pareto front using as few of these expensive simulations as possible. Here, we describe an optimization approach based on surrogate models and diverse sampling strategies to accelerate the search for the Pareto solutions. We use a separate surrogate model for approximating each objective function and then we use the surrogate models to inform where additional expensive simulations should be run. The surrogate models are updated in an active learning framework whenever new information from the expensive simulations becomes available. The sampling strategies aim at balancing local improvements of the approximate Pareto front and global exploration to identify the extrema and fill in large gaps of the approximate Pareto front. We demonstrate on a large set of benchmark problems the effectiveness of the method for finding good approximations of the Pareto front.
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 GP-UCB algorithm, but the additional random exploration step accelerates their convergence, nearly achieving the optimal convergence rate. Furthermore, to facilitate Bayesian inference with intractable likelihoods, we propose to utilize optimization iterates for maximum a posteriori estimation to build a Gaussian process surrogate model for the unnormalized log-posterior density. We provide bounds for the Hellinger distance between the true and the approximate posterior distributions in terms of the number of design points. We demonstrate the effectiveness of our Bayesian optimization algorithms in nonconvex benchmark objective functions, in a machine learning hyperparameter tuning problem, and in a black-box engineering design problem. The effectiveness of our posterior approximation approach is demonstrated in two Bayesian inference problems for parameters of dynamical systems.
Due to the distributed nature of Federated Learning (FL) systems, each local client has access to the global model, which poses a critical risk of model leakage. Existing works have explored injecting watermarks into local models to enable intellectual property protection. However, these methods either focus on non-traceable watermarks or traceable but white-box watermarks. We identify a gap in the literature regarding the formal definition of traceable black-box watermarking and the formulation of the problem of injecting such watermarks into FL systems. In this work, we first formalize the problem of injecting traceable black-box watermarks into FL. Based on the problem, we propose a novel server-side watermarking method, TraMark, which creates a traceable watermarked model for each client, enabling verification of model leakage in black-box settings. To achieve this, TraMark partitions the model parameter space into two distinct regions: the main task region and the watermarking region. Subsequently, a personalized global model is constructed for each client by aggregating only the main task region while preserving the watermarking region. Each model then learns a unique watermark exclusively within the watermarking region using a distinct watermark dataset before being sent back to the local client. Extensive results across various FL systems demonstrate that TraMark ensures the traceability of all watermarked models while preserving their main task performance.
The objective of this report is threefold. First, it details a method for deriving a semi-analytic solution to the Noh Problem when using a “black-box” equation of state. Such capability allows us to perform verification on complicated, more realistic equations of state. Examples include Steinberg equations of state for materials and tabulated equations of state. The second objective is to apply the methodology to verify the singularity-eos equation of state library. We do so by solving the Rankine-Hugoinot jump conditions for the Noh Problem, ensuring singularity derives the correct solution and comparing the error to an exact implementation of the equation of state. The third objective is to perform verification of the xRAGE Eulerian hydrodynamics code when interfaced with singularity. We provide the theory, analysis, documentation for a python implementation of the proposed solver, and verification results.
The multireference coupled-cluster Monte Carlo (MR-CCMC) algorithm is a determinant-based quantum Monte Carlo (QMC) algorithm that is conceptually similar to Full Configuration Interaction QMC (FCIQMC). It has been shown to offer a balanced treatment of both static and dynamic correlation while retaining polynomial scaling, although application to large systems with significant strong correlation remained impractical. In this paper, we document recent algorithmic advances that enable rapid convergence and a more black-box approach to the multireference problem. These include a logarithmically scaling metric-tree-based excitation acceptance algorithm to search for determinants connected to the reference space at the desired excitation level and a symmetry-screening procedure for the reference space. We show that, for moderately sized reference spaces, the new search algorithm brings about an approximately 8-fold acceleration of one MR-CCMC iteration, while the symmetry screening procedure reduces the number of active reference space determinants with essentially no loss of accuracy. We also introduce a stochastic implementation of an approximate wall projector, which is the infinite imaginary time limit of the exponential projector, using a truncated expansion of the wall function in Chebyshev polynomials. Notably, this wall-Chebyshev projector can be used to accelerate any projector-based QMC algorithm. We show that it requires significantly fewer applications of the Hamiltonian to achieve the same statistical convergence. We benchmark these acceleration methods on the beryllium and carbon dimers, using initiator FCIQMC and MR-CCMC with basis sets up to cc-pVQZ quality.
Tuning algorithmic parameters to optimize the performance of large, complicated computational codes is an important problem involving finding the optima and identifying regimes defined by non-smooth boundaries in black-box functions. Within the Bayesian optimization framework, the Gaussian process surrogate model produces smooth mean functions, but functions in the tuning problem are often non-smooth, which is exacerbated by the fact that we usually have limited sequential samples from the black-box function. Here, motivated by these issues encountered in tuning, we propose a novel Gaussian process model called a clustered Gaussian process (cGP), where the components are dynamically updated by clustering. In our studies, the performance of cGP can be better than stationary GPs in nearly 90% of the experiments and better than non-stationary GPs in nearly 70% of the repeated experiments while requiring less computational cost. cGP provides a novel approach for dynamic GP, computes more efficiently than recursive partitioning, and discovers non-smoothness regimes. We provide extensive experiments including high-performance computing (HPC) and industrial simulation functions to show the effectiveness of our methods.
Multiobjective simulation optimization (MOSO) problems are optimization problems with multiple conflicting objectives, where evaluation of at least one of the objectives depends on a black-box numerical code or real-world experiment, which we refer to as a simulation. Whereas an extensive body of research is dedicated to developing new algorithms and methods for solving these and related problems, it is challenging and time-consuming to integrate these techniques into real-world production-ready solvers. This is partly because of the diversity and complexity of modern state-of-the-art MOSO algorithms and methods and partly because of the complexity and specificity of many real-world problems and their corresponding computing environments. The complexity of this problem is only compounded when introducing potentially complex and/or domain-specific surrogate-modeling techniques, problem formulations, design spaces, and data acquisition functions. Here, this paper carefully surveys the current state of the art in MOSO algorithms, techniques, and solvers, as well as problem types and computational environments where MOSO is commonly applied. We then present several key challenges in the design of a parallel multiobjective simulation optimization framework (ParMOO) and how they have been addressed. Finally, we provide two case studies demonstrating how customized ParMOO solvers can be quickly built and deployed to solve real-world MOSO problems.
Neural networks have emerged as powerful tools for mapping between inputs and outputs. However, their black-box nature limits the ability to encode or impose specific structural relationships between inputs and outputs. Many scientific and engineering problems, such as constitutive modeling in solid mechanics, require networks that can enforce convexity, monotonicity, or other structural constraints to ensure physical consistency. Here, we introduce the Input Specific Neural Network (ISNN), a new architecture that enables multiple, distinct constraints to be imposed on different input subsets for scalar-valued outputs. This framework unifies convex, monotone–convex, monotone, and arbitrary mappings within a single network for the first time. Two ISNN architectures with analytical first- and second-order derivatives are developed. We demonstrate the performance on synthetic toy problems, inverse problems in isotropic hyperelasticity, and finite element simulations. ISNNs achieve improved extrapolation behavior, require fewer invariant inputs than standard input convex networks for polyconvex potentials, and enable significant computational savings via manual differentiation. We also show how ISNNs can be used to learn structural relationships between inputs and outputs via a binary gating mechanism. Particularly, ISNNs are employed to model a homogenized anisotropic free energy potential in a decoupled multiscale setting. The network learns whether or not the potential should be modeled as polyconvex and retains only the relevant layers while using the minimum number of inputs. ISNNs provide a flexible foundation for embedding structural priors into neural networks, enhancing both interpretability and stability. They are broadly applicable across computational mechanics and other scientific domains requiring constrained functional relationships.
The objective of this paper is to derive a method of constructing semi-analytic solutions to the Noh problem when the equation of state is a black box. Such solutions can be used for verification tests of hydrodynamics codes. We present the underlying theory, the method for finding solutions, and several examples of derived semi-analytic solutions. We end by performing a classic verification convergence test comparing numerical results from a hydrodynamics code against a non-trivial semi-analytic solution.
In quantum embedding theories, a quantum many-body system is divided into localized clusters of sites which are treated with an accurate ‘high-level’ theory and glued together self-consistently by a less accurate ‘low-level’ theory at the global scale. The recently introduced variational embedding approach for quantum many-body problems combines the insights of semidefinite relaxation and quantum embedding theory to provide a lower bound on the ground-state energy that improves as the cluster size is increased. The variational embedding method is formulated as a semidefinite program (SDP), which can suffer from poor computational scaling when treated with black-box solvers. Here, we exploit the interpretation of this SDP as an embedding method to develop an algorithm which alternates parallelizable local updates of the high-level quantities with updates that enforce the low-level global constraints. Moreover, we show how translation invariance in lattice systems can be exploited to reduce the complexity of projecting a key matrix to the positive semidefinite cone.
Water chemistry plays a critical role in the design and operation of water treatment processes. Detailed chemistry modeling tools use a combination of advanced thermodynamic models and extensive databases to predict phase equilibria and reaction phenomena. The complexity and formulation of these models preclude their direct integration in equation-oriented modeling platforms, making it difficult to use their capabilities for rigorous water treatment process optimization. Neural networks (NN) can provide a pathway for integrating the predictive capability of chemistry software into equation-oriented models and enable optimization of complex water treatment processes across a broad range of conditions and process designs. Herein, we assess how NN architecture and training data impact their accuracy and use in equation-oriented water treatment models. We generate training data using PhreeqC software and determine how data generation and sample size impact the accuracy of trained NNs. The effect of NN architecture on optimization is evaluated by optimizing hypothetical black-box desalination processes using a range of feed compositions from USGS brackish water data set, tracking the number of successful optimizations, and testing the impact of initial guess on the final solution. Our results clearly demonstrate that data generation and architecture impact NN accuracy and viability for use in equation-oriented optimization problems.
Machine learning (ML)-based black-box optimization algorithms have demonstrated significant improvements in accelerator optimization speed, often by orders of magnitude. However, deploying these algorithms in real-time facility control remains challenging due to the specialized expertise and infrastructure required. To bridge this gap, we introduce the Xopt ecosystem, a versatile suite of tools designed to make advanced ML-based optimization accessible to the broader accelerator community. This ecosystem includes Xopt, a modular Python framework that facilitates the integration of ML-based optimization algorithms with arbitrary control problems, and Badger, a graphical user interface built on top of Xopt, which enables seamless deployment of ML algorithms in real-time control systems. The Xopt ecosystem has been successfully applied towards solving challenging real-time control problems at leading international accelerator facilities, including SLAC, LBNL, Argonne, Fermilab, BNL, DESY, and ESRF, demonstrating its effectiveness in real-world optimization tasks. In this presentation, we provide an overview of Xopt’s capabilities and illustrate its impact through case studies from SLAC accelerator facilities including LCLS, LCLS-II, and FACET-II.
Diffusion MRI (dMRI) non-invasively maps brain white matter yet necessitates denoising due to low signal-to-noise ratios. Patch2Self (P2S) employing self-supervised techniques and regression on a Casorati matrix effectively denoises dMRI images and has become the new de-facto standard in this field. P2S however is resource intensive both in terms of running time and memory usage as it uses all voxels (n) from all-but-one held-in volumes (d-1) to learn a linear mapping Phi : \mathbb R ^ n x(d-1) \mapsto \mathbb R ^ n for denoising the held-out volume. The increasing size and dimensionality of higher resolution dMRI acquisitions can make P2S infeasible for large-scale analyses. This work exploits the redundancy imposed by P2S to alleviate its performance issues and inspect regions that influence the noise disproportionately. Specifically this study makes a three-fold contribution: (1) We present Patch2Self2 (P2S2) a method that uses matrix sketching to perform self-supervised denoising. By solving a sub-problem on a smaller sub-space so called coreset we show how P2S2 can yield a significant speedup in training time while using less memory. (2) We present a theoretical analysis of P2S2 focusing on determining the optimal sketch size through rank estimation a key step in achieving a balance between denoising accuracy and computational efficiency. (3) We show how the so-called statistical leverage scores can be used to interpret the denoising of dMRI data a process that was traditionally treated as a black-box. Experimental results on both simulated and real data affirm that P2S2 maintains denoising quality while significantly enhancing speed and memory efficiency achieved by training on a reduced data subset.
Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.
Time-dependent electromagnetic drives are fundamental for controlling complex quantum systems, including superconducting Josephson circuits. In these devices, accurate time-dependent Hamiltonian models are imperative for predicting their dynamics and designing high-fidelity quantum operations. Existing numerical methods, such as black-box quantization (BBQ) and energy-participation ratio (EPR), excel at modeling the static Hamiltonians of Josephson circuits. However, these techniques do not fully capture the behavior of driven circuits stimulated by external microwave drives, nor do they include a generalized approach to account for the inevitable noise and dissipation that enter through microwave ports. Here, we introduce numerical techniques that leverage classical microwave simulations, efficiently executable in finite-element solvers, to obtain the time-dependent Hamiltonian of microwave-driven superconducting circuits with arbitrary geometries under charge, flux, or mixed electromagnetic modulation. Importantly, our techniques do not rely on a lumped-element description of the superconducting circuit, in contrast to previous approaches to tackling this problem. We demonstrate the versatility of our approach by characterizing the driven properties of realistic circuit devices in complex electromagnetic environments, including coherent dynamics due to charge and flux modulation, as well as drive-induced relaxation and dephasing. Our techniques offer a powerful toolbox for optimizing circuit designs and advancing practical applications in superconducting quantum computing.
Abstract Although beam emittance is critical for the performance of high-brightness accelerators, optimization is often time limited as emittance calculations, commonly done via quadrupole scans, are typically slow. Such calculations are a type of multipoint query , i.e. each query requires multiple secondary measurements. Traditional black-box optimizers such as Bayesian optimization are slow and inefficient when dealing with such objectives as they must acquire the full series of measurements, but return only the emittance, with each query. We propose a new information-theoretic algorithm, Multipoint-BAX , for black-box optimization on multipoint queries, which queries and models individual beam-size measurements using techniques from Bayesian Algorithm Execution (BAX). Our method avoids the slow multipoint query on the accelerator by acquiring points through a virtual objective , i.e. calculating the emittance objective from a fast learned model rather than directly from the accelerator. We use Multipoint-BAX to minimize emittance at the Linac Coherent Light Source (LCLS) and the Facility for Advanced Accelerator Experimental Tests II (FACET-II). In simulation, our method is 20× faster and more robust to noise compared to existing methods. In live tests, it matched the hand-tuned emittance at FACET-II and achieved a 24% lower emittance than hand-tuning at LCLS. Our method represents a conceptual shift for optimizing multipoint queries, and we anticipate that it can be readily adapted to similar problems in particle accelerators and other scientific instruments.
The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.