Surrogate modeling has brought about a revolution in computation in the branches of science and engineering. Backed by Artificial Intelligence, a surrogate model can present highly accurate results with a significant reduction in computation time than computer simulation of actual models. Surrogate modeling techniques have found their use in numerous branches of science and engineering, energy system modeling being one of them. Since the idea of hybrid and sustainable energy systems is spreading rapidly in the modern world for the paradigm of the smart energy shift, researchers are exploring the future application of artificial intelligence-based surrogate modeling in analyzing and optimizing hybrid energy systems. One of the promising technologies for assessing applicability for the energy system is the digital twin, which can leverage surrogate modeling. This work presents a comprehensive framework/review on Artificial Intelligence-driven surrogate modeling and its applications with a focus on the digital twin framework and energy systems. The role of machine learning and artificial intelligence in constructing an effective surrogate model is explained. After that, different surrogate models developed for different sustainable energy sources are presented. Finally, digital twin surrogate models and associated uncertainties are described.

The shuffled linear regression problem aims to recover linear relationships in datasets where the correspondence between input and output is unknown. This problem arises in a wide range of applications including survey data, in which one needs to decide whether the anonymity of the responses can be preserved while uncovering significant statistical connections. In this work, we propose a novel optimization algorithm for shuffled linear regression based on a posterior-maximizing objective function assuming Gaussian noise prior. We compare and contrast our approach with existing methods on synthetic and real data. We show that our approach performs competitively while achieving empirical running-time improvements. Furthermore, we demonstrate that our algorithm is able to utilize the side information in the form of seeds, which recently came to prominence in related problems.

This paper considers safe control synthesis for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and the safety constraints. We formulate novel probabilistic and robust (worst-case) control Lyapunov function (CLF) and control barrier function (CBF) constraints that take into account the effect of uncertainty in either case. We show that either the probabilistic or the robust (worst-case) formulation leads to a second-order cone program (SOCP), which enables efficient safe and stable control synthesis. We evaluate our approach in PyBullet simulations of an autonomous robot navigating in unknown environments and compare the performance with a baseline CLF-CBF quadratic programming approach.

Bayesian optimization is a powerful collection of methods for optimizing stochastic expensive black box functions. One key component of a Bayesian optimization algorithm is the acquisition function that determines which solution should be evaluated in every iteration. A popular and very effective choice is the Knowledge Gradient acquisition function, however there is no analytical way to compute it. Several different implementations make different approximations. In this paper, we review and compare the spectrum of Knowledge Gradient implementations and propose One-shot Hybrid KG, a new approach that combines several of the previously proposed ideas and is cheap to compute as well as powerful and efficient. We prove the new method preserves theoretical properties of previous methods and empirically show the drastically reduced computational overhead with equal or improved performance. All experiments are implemented in BOTorch and code is available on github.

Some boosting algorithms, such as LPBoost, ERLPBoost, and C-ERLPBoost, aim to solve the soft margin optimization problem with the $\ell_1$-norm regularization. LPBoost rapidly converges to an $\epsilon$-approximate solution in practice, but it is known to take $\Omega(m)$ iterations in the worst case, where $m$ is the sample size. On the other hand, ERLPBoost and C-ERLPBoost are guaranteed to converge to an $\epsilon$-approximate solution in $O(\frac{1}{\epsilon^2} \ln \frac{m}{\nu})$ iterations. However, the computation per iteration is very high compared to LPBoost. To address this issue, we propose a generic boosting scheme that combines the Frank-Wolfe algorithm and any secondary algorithm and switches one to the other iteratively. We show that the scheme retains the same convergence guarantee as ERLPBoost and C-ERLPBoost. One can incorporate any secondary algorithm to improve in practice. This scheme comes from a unified view of boosting algorithms for soft margin optimization. More specifically, we show that LPBoost, ERLPBoost, and C-ERLPBoost are instances of the Frank-Wolfe algorithm. In experiments on real datasets, one of the instances of our scheme exploits the better updates of the secondary algorithm and performs comparably with LPBoost.

The NP-hard problem of optimizing a shallow ReLU network can be characterized as a combinatorial search over each training example's activation pattern followed by a constrained convex problem given a fixed set of activation patterns. We explore the implications of this combinatorial aspect of ReLU optimization in this work. We show that it can be naturally modeled via a geometric and combinatoric object known as a zonotope with its vertex set isomorphic to the set of feasible activation patterns. This assists in analysis and provides a foundation for further research. We demonstrate its usefulness when we explore the sensitivity of the optimal loss to perturbations of the training data. Later we discuss methods of zonotope vertex selection and its relevance to optimization. Overparameterization assists in training by making a randomly chosen vertex more likely to contain a good solution. We then introduce a novel polynomial-time vertex selection procedure that provably picks a vertex containing the global optimum using only double the minimum number of parameters required to fit the data. We further introduce a local greedy search heuristic over zonotope vertices and demonstrate that it outperforms gradient descent on underparameterized problems.

Training deep neural networks (DNNs) is becoming increasingly more resource- and energy-intensive every year. Unfortunately, existing works primarily focus on optimizing DNN training for faster completion, often without considering the impact on energy efficiency. In this paper, we observe that common practices to improve training performance can often lead to inefficient energy usage. More importantly, we demonstrate that there is a tradeoff between energy consumption and performance optimization. To this end, we propose Zeus, an optimization framework to navigate this tradeoff by automatically finding optimal job- and GPU-level configurations for recurring DNN training jobs. Zeus uses an online exploration-exploitation approach in conjunction with just-in-time energy profiling, averting the need for expensive offline measurements, while adapting to data drifts over time. Our evaluation shows that Zeus can improve the energy efficiency of DNN training by 15.3%-75.8% for diverse workloads.

We consider the distributed stochastic optimization problem where $n$ agents want to minimize a global function given by the sum of agents' local functions, and focus on the heterogeneous setting when agents' local functions are defined over non-i.i.d. data sets. We study the Local SGD method, where agents perform a number of local stochastic gradient steps and occasionally communicate with a central node to improve their local optimization tasks. We analyze the effect of local steps on the convergence rate and the communication complexity of Local SGD. In particular, instead of assuming a fixed number of local steps across all communication rounds, we allow the number of local steps during the $i$-th communication round, $H_i$, to be different and arbitrary numbers. Our main contribution is to characterize the convergence rate of Local SGD as a function of $\{H_i\}_{i=1}^R$ under various settings of strongly convex, convex, and nonconvex local functions, where $R$ is the total number of communication rounds. Based on this characterization, we provide sufficient conditions on the sequence $\{H_i\}_{i=1}^R$ such that Local SGD can achieve linear speed-up with respect to the number of workers. Furthermore, we propose a new communication strategy with increasing local steps superior to existing communication strategies for strongly convex local functions. On the other hand, for convex and nonconvex local functions, we argue that fixed local steps are the best communication strategy for Local SGD and recover state-of-the-art convergence rate results. Finally, we justify our theoretical results through extensive numerical experiments.

We propose the new task of K principal concept identification for dataset summarizarion. The objective is to find a set of K concepts that best explain the variation within the dataset. Concepts are high-level human interpretable terms such as "tiger", "kayaking" or "happy". The K concepts are selected from a (potentially long) input list of candidates, which we denote the concept-bank. The concept-bank may be taken from a generic dictionary or constructed by task-specific prior knowledge. An image-language embedding method (e.g. CLIP) is used to map the images and the concept-bank into a shared feature space. To select the K concepts that best explain the data, we formulate our problem as a K-uncapacitated facility location problem. An efficient optimization technique is used to scale the local search algorithm to very large concept-banks. The output of our method is a set of K principal concepts that summarize the dataset. Our approach provides a more explicit summary in comparison to selecting K representative images, which are often ambiguous. As a further application of our method, the K principal concepts can be used to classify the dataset into K groups. Extensive experiments demonstrate the efficacy of our approach.

We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose marginal distributions on $X_0,X_1$ equals $\pi_0,\pi_1$, respectively, where $c$ is a cost function. Our method iteratively constructs a sequence of neural ordinary differentiable equations (ODE), each learned by solving a simple unconstrained regression problem, which monotonically reduce the transport cost while automatically preserving the marginal constraints. This yields a monotonic interior approach that traverses inside the set of valid couplings to decrease the transport cost, which distinguishes itself from most existing approaches that enforce the coupling constraints from the outside. The main idea of the method draws from rectified flow, a recent approach that simultaneously decreases the whole family of transport costs induced by convex functions $c$ (and is hence multi-objective in nature), but is not tailored to minimize a specific transport cost. Our method is a single-object variant of rectified flow that guarantees to solve the OT problem for a fixed, user-specified convex cost function $c$.