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The presentation summarizes part of our work on the PrOMMiS project. It describes a systematic benchmarking activity of data-driven optimization algorithms for self-driving laboratories in critical materials manufacturing.
This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.
Abstract not provided.
Traditional NNs often lack the ability for uncertainty quantification. Bayesian NNs(BNNs) could help measure the confidence level by using distributions in NNs modeling. Besides, knowledge is commonly available and could improve the performance of BNNs if it can be properly incorporated. In this work, we propose a novel Posterior-Regularized BNN(PR-BNN) model by incorporating soft and hard constraints as a posterior regularization term. We also propose an augmented Lagrangian method and stochastic optimization algorithm for efficient updating via Monte Carlo sampling. The simulations and case studies in solar energy prediction have shown the performance improvement of the proposed model over traditional BNNs.
Process optimization is the discipline of adjusting a process to optimize a specified set of parameters without violating engineering constraints. This article reviews data-driven optimization methods based on genetic algorithms and stochastic models and demonstrates their use in powder-bed fusion and directed energy deposition processes. In the latter case, closed-loop feedback is used to control melt pool temperature and cooling rate in order to achieve desired microstructure.
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $\mathcal{O}$(T 2 x polylog($n$)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.
Bayesian state estimation of a dynamical system from a stream of noisy measurements is important in many geophysical and engineering applications where high dimensionality of the state space, sparse observations, and model error pose key challenges. In this work, three computationally feasible, approximate Gaussian data assimilation/filtering algorithms are considered in various regimes of turbulent 2D Navier--Stokes dynamics in the presence of model error. The first source of error arises from the necessary use of reduced models for the forward dynamics of the filters, while a particular type of representation error arises from the finite resolution of observations which mix up information about resolved and unresolved dynamics. Two stochastically parameterized filtering algorithms, referred to as cSPEKF and GCF, are compared with 3DVAR---a prototypical time-sequential algorithm known to be accurate for filtering dissipative systems for a suitably inflated “background” covariance. We provide the first evidence that the stochastically parameterized algorithms, which do not rely on detailed knowledge of the underlying dynamics and do not require covariance inflation, can compete with or outperform an optimally tuned 3DVAR algorithm, and they can overcome competing sources of error in a range of dynamical scenarios.
To take unit commitment (UC) decisions under uncertain load, most existing stochastic optimization (SO) frameworks adopt a generic representation of uncertainty. While load levels that materialize on a particular day are influenced by various covariates (such as the day of the week or temperature), SO frameworks typically disregard such side observations, wasting actionable information that could significantly enhance decision quality. Here, this article proposes a contextual SO (CSO) framework for UC under uncertain load, which can effectively exploit covariate observations in conjunction with a class of machine learning (ML) algorithms to improve the out-of-sample performance of UC decisions. It shows how three ML algorithms, adaptive boosting, gradient boosted trees, and extreme gradient boosting, can be used to this end, constituting the first application of these algorithms in any CSO framework. Using real-world data harvested from the New York ISO grid, we measure the out-of-sample performance of the framework in terms of total operation cost, shed load values, locational marginal prices, and total payments by the loads, against several benchmark methods proposed in the literature. The article has an online companion (Yurdakul et al.), wherein we present additional results and lay out further mathematical formulations used in this work.
This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.
Abstract The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.
Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025
Lagrangian particle methods based on detailed atomic and molecular and nanoscale systems. However, the maximum time step is limited by the smallest oscillation period of the fastest atomic motion, rendering long-time simulations very expensive. To resolve this bottleneck, we propose a supervised parallel-in-time algorithm for stochastic dynamics to accelerate long-time Lagrangian particle simulations. Our method is inspired by bottom-up coarse-graining projections that yield mean-field hydrodynamic behavior in the continuum limit.
Recent advances in deterministic unit commitment, both formulaic and algorithmic, along with modern algorithmic approaches for stochastic programming, have enabled the solution of stochastic unit commitment problems with hundreds of scenarios on large-scale transmission networks. In this presentation, we will give an overview of these methods, including lazy transmission constraint generation, lower-bounding techniques, and heuristics, all of which can be executed in concert with customized decomposition approaches for optimization under uncertainty. We demonstrate the effectiveness of these techniques on the TAMU Texas7K synthetic transmission network, leveraging realistic high-resolution forecasts based on NREL renewable resource availability data. The software leveraged for these demonstrations is available via the open-source software packages EGRET (for electrical grid optimization) and mpi-sppy (for optimization under uncertainty).
Here, we propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolerance is satisfied. CMLMC assumes discretization hierarchies that are defined a priori for each level and are geometrically refined across levels. Moreover, the actual choice of computational work across levels is based on parametric models for the average cost per sample and the corresponding variance and weak error. These parameters are calibrated using Bayesian estimation, taking particular notice of the deepest levels of the discretization hierarchy, where only few realizations are available to produce the estimates. The resulting CMLMC estimator exhibits a non-trivial splitting between bias and statistical contributions. We also show the asymptotic normality of the statistical error in the MLMC estimator and justify in this way our error estimate that allows prescribing both required accuracy and confidence in the final result. Our numerical results substantiate the above results and illustrate the corresponding computational savings in examples that are described in terms of differential equations either driven by random measures or with random coefficients.
This article addresses the problem of wake steering control for wind farms that explicitly consider the tradeoff between farm-level power generation and yaw duty cycle under variable and uncertain wind conditions. A novel stochastic model predictive control (MPC) algorithm is presented, which utilizes a stochastic model of the freestream wind field components in a receding horizon framework to compute optimal yaw set points that maximize the expected value of the farm power while constraining the yaw actuation. Different configurations of the algorithm are evaluated using a steady-state wind farm simulator. The proposed stochastic MPC algorithm can plan control actions over a future prediction horizon based on probabilistic estimates of the incoming wind magnitude and direction.
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify optimal and near-optimal approximations in terms of Kullback-Leibler divergence. The user-chosen sparsity trades off the quality of the approximation against visual conciseness and computational tractability. One class of approximations contains graphs with speci ed in-degrees. Another class additionally requires that the graph is connected. For both classes, we propose algorithms to identify the optimal approximations and also near-optimal approximations, using a novel relaxation of submodularity. We also propose algorithms to identify the r-best approximations among these classes, enabling robust decision making.
In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. For a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2 ), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.
Non-conservative processes play a fundamental role in plasticity and are behind important macroscopic phenomena such as creep, dynamic strain aging, loop raft formation, etc. In the most general case, vacancy-induced dislocation climb is the operating unit mechanism. While dislocation/vacancy interactions have been modeled in the literature using a variety of methods, the approaches developed rely on continuum descriptions of both the vacancy population and its fluxes. However, there are numerous situations in physics where point defect populations display heterogeneous concentrations and/or non-smooth kinetics. Here, a kinetic Monte Carlo (kMC) approach for modeling vacancy transport in response to arbitrary stress fields is used. Vacancies are treated as point particles and are coupled to the dislocation substructure representing a deformed material via an advection term defined by the local stress gradients. The stress fields and the dislocation substructure are evolved using a discrete dislocation dynamics (DDD) module. To extend the coupled model to the treatment of large systems, we have implemented it in the massively-parallel DDD code ParaDiS. To avoid numerical incompatibilities associated with merging deterministic (DDD) and stochastic (kMC) integration algorithms, we cast the entire elasto-plastic-diffusive problem within a single stochastic framework, taking advantage of a parallel kMC algorithm to evolve the system as a single event-driven process. The large-scale implementation enables the study of the evolution of a variety of dislocation-defect scenarios governed by non-conservative transport kinetics. After carrying out an exhaustive numerical and computational analysis of our parallel algorithm, we show results that emphasize situations where inhomogeneous vacancy dynamics are of relevance, and compare discrete kinetics to continuum solutions for several cases.