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The semi-empirical nature of best-estimate models closing the balance equations of thermal-hydraulic (TH) system codes is well-known as a significant source of uncertainty for accuracy of output predictions. This uncertainty, called model uncertainty, is usually represented by multiplicative (log-)Gaussian variables whose estimation requires solving an inverse problem based on a set of adequately chosen real experiments. One method from the TH field, called CIRCE, addresses it. We present in the paper a generalization of this method to several groups of experiments each having their own properties, including different ranges for input conditions and different geometries. An individual (log-)Gaussian distribution is therefore estimated for each group in order to investigate whether the model uncertainty is homogeneous between the groups, or should depend on the group. To this end, a multi-group CIRCE is proposed where a variance parameter is estimated for each group jointly to a mean parameter common to all the groups to preserve the uniqueness of the best-estimate model. The ECME algorithm for Maximum Likelihood Estimation is adapted to the latter context, then applied to relevant demonstration cases. Finally, it is tested on a practical case to assess the uncertainty of critical mass flow assuming two groups due to the difference of geometry between the experimental setups.

Hyperparameter optimization (HPO) is an important step in machine learning (ML) model development, but common practices are archaic -- primarily relying on manual or grid searches. This is partly because adopting advanced HPO algorithms introduces added complexity to the workflow, leading to longer computation times. This poses a notable challenge to ML applications, as suboptimal hyperparameter selections curtail the potential of ML model performance, ultimately obstructing the full exploitation of ML techniques. In this article, we present a two-step HPO method as a strategic solution to curbing computational demands and wait times, gleaned from practical experiences in applied ML parameterization work. The initial phase involves a preliminary evaluation of hyperparameters on a small subset of the training dataset, followed by a re-evaluation of the top-performing candidate models post-retraining with the entire training dataset. This two-step HPO method is universally applicable across HPO search algorithms, and we argue it has attractive efficiency gains. As a case study, we present our recent application of the two-step HPO method to the development of neural network emulators for aerosol activation. Although our primary use case is a data-rich limit with many millions of samples, we also find that using up to 0.0025% of the data (a few thousand samples) in the initial step is sufficient to find optimal hyperparameter configurations from much more extensive sampling, achieving up to 135-times speedup. The benefits of this method materialize through an assessment of hyperparameters and model performance, revealing the minimal model complexity required to achieve the best performance. The assortment of top-performing models harvested from the HPO process allows us to choose a high-performing model with a low inference cost for efficient use in global climate models (GCMs).

Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step algorithm coupled with a solid dynamic relaxation scheme. The explicit scheme simplifies the equation system in contrast to the implicit scheme, while the multi-time step algorithm allows the equations of different physical processes to be solved under different time step sizes. Furthermore, an implicit viscous damping relaxation technique is applied to significantly reduce computational iterations required to achieve equilibrium in the comparatively fast solid response process. To validate the accuracy and efficiency of the proposed algorithm, two distinct scenarios, i.e., a nonlinear hardening bar stretching and a fluid diffusion coupled with Nafion membrane flexure, are simulated. The results show good agreement with experimental data and results from other numerical methods, and the simulation time is reduced firstly by independently addressing different processes with the multi-time step algorithm and secondly decreasing solid dynamic relaxation time through the incorporation of damping techniques.

Multiscale stochastic dynamical systems have been widely adopted to scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective reduced dynamics for a slow-fast stochastic dynamical system. Given observation data on a short-term period satisfying some unknown slow-fast stochastic system, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also proved to be accurate, stable and effective through numerical experiments under various evaluation metrics.

Motion planning is the soul of robot decision making. Classical planning algorithms like graph search and reaction-based algorithms face challenges in cases of dense and dynamic obstacles. Deep learning algorithms generate suboptimal one-step predictions that cause many collisions. Reinforcement learning algorithms generate optimal or near-optimal time-sequential predictions. However, they suffer from slow convergence, suboptimal converged results, and overfittings. This paper introduces a hybrid algorithm for robotic motion planning: long short-term memory (LSTM) pooling and skip connection for attention-based discrete soft actor critic (LSA-DSAC). First, graph network (relational graph) and attention network (attention weight) interpret the environmental state for the learning of the discrete soft actor critic algorithm. The expressive power of attention network outperforms that of graph in our task by difference analysis of these two representation methods. However, attention based DSAC faces the overfitting problem in training. Second, the skip connection method is integrated to attention based DSAC to mitigate overfitting and improve convergence speed. Third, LSTM pooling is taken to replace the sum operator of attention weigh and eliminate overfitting by slightly sacrificing convergence speed at early-stage training. Experiments show that LSA-DSAC outperforms the state-of-the-art in training and most evaluations. The physical robot is also implemented and tested in the real world.

A novel and fully distributed optimization method is proposed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network without imposing any differentiability assumptions. Firstly, a tractable approximated DRCP (ADRCP) is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints and restricting the right-hand side of the constraints with a proper positive parameter, which will be iteratively solved by a random-fixed projection algorithm. Secondly, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed feasibility. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and populating the cutting-surfaces into the existing finite set of constraints. Thirdly, to ensure finite-time convergence of the distributed optimization, a distributed termination algorithm is developed based on uniformly local consensus and zeroth-order optimality under uniformly strongly connected graphs. Fourthly, it is proved that the cutting-surface consensus approach converges within a finite number of iterations. Finally, the effectiveness of the approach is illustrated through a numerical example.

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 $\mathcal{O}(T^2 \times \text{polylog}(n))$, 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.

The utility of reinforcement learning is limited by the alignment of reward functions with the interests of human stakeholders. One promising method for alignment is to learn the reward function from human-generated preferences between pairs of trajectory segments, a type of reinforcement learning from human feedback (RLHF). These human preferences are typically assumed to be informed solely by partial return, the sum of rewards along each segment. We find this assumption to be flawed and propose modeling human preferences instead as informed by each segment's regret, a measure of a segment's deviation from optimal decision-making. Given infinitely many preferences generated according to regret, we prove that we can identify a reward function equivalent to the reward function that generated those preferences, and we prove that the previous partial return model lacks this identifiability property in multiple contexts. We empirically show that our proposed regret preference model outperforms the partial return preference model with finite training data in otherwise the same setting. Additionally, we find that our proposed regret preference model better predicts real human preferences and also learns reward functions from these preferences that lead to policies that are better human-aligned. Overall, this work establishes that the choice of preference model is impactful, and our proposed regret preference model provides an improvement upon a core assumption of recent research. We have open sourced our experimental code, the human preferences dataset we gathered, and our training and preference elicitation interfaces for gathering a such a dataset.

An efficient method of computing power expansions of algebraic functions is the method of Kung and Traub and is based on exact arithmetic. This paper shows a numeric approach is both feasible and accurate while also introducing a performance improvement to Kung and Traub's method based on the ramification extent of the expansions. A new method is then described for computing radii of convergence using a series comparison test. Series accuracies are then fitted to a simple log-linear function in their domain of convergence and found to have low variance. Algebraic functions up to degree 50 were analyzed and timed. A consequence of this work provided a simple method of computing the Riemann surface genus and was used as a cycle check-sum. Mathematica ver. 13.2 was used to acquire and analyze the data on a 4.0 GHz quad-core desktop computer.