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Concentrating Solar Power Tower (CSPT) plants rely on heliostat fields to focus sunlight onto a central receiver. Although simple aiming strategies, such as directing all heliostats to the receivers equator, can maximize energy collection, they often result in uneven flux distributions that lead to hotspots, thermal stresses, and reduced receiver lifetimes. This paper presents a novel, data-driven approach that integrates constraint learning, neural network-based surrogates, and mathematical optimization to overcome these challenges. The methodology learns complex heliostat-to-receiver flux interactions from simulation data, constructing a surrogate model that is embedded into a tractable optimization framework. By maximizing a tailored quality score that balances energy collection and flux uniformity, the approach yields smoothly distributed flux profiles and mitigates excessive thermal peaks. An iterative refinement process, guided by the trust region and progressive data sampling, ensures the surrogate model improves the obtained solution by exploring new spaces during the iterations. Results from a real CSPT case study demonstrate that the proposed approach surpasses conventional heuristic methods, offering flatter flux distributions and safer thermal conditions without a substantial loss in overall energy capture.

We study the double homology associated to triangulated spheres and present two results. First, we explicitly compute the double homology for minimum degree sphere triangulations. Using a spectral sequence argument, we compute the effect of removing a maximal simplex of a non-neighborly sphere triangulation. Using these results and computational aid we generate complexes with exotic double homology rank. We also relate the double homology of a complex with how neighborly it is., Comment: 19 Pages. Clarified some of the proofs in the previous version, added more results regarding 2-spheres and neighborly spheres

Accurate 3D object detection is crucial to autonomous driving. Though LiDAR-based detectors have achieved impressive performance, the high cost of LiDAR sensors precludes their widespread adoption in affordable vehicles. Camera-based detectors are cheaper alternatives but often suffer inferior performance compared to their LiDAR-based counterparts due to inherent depth ambiguities in images. In this work, we seek to improve monocular 3D detectors by leveraging unlabeled historical LiDAR data. Specifically, at inference time, we assume that the camera-based detectors have access to multiple unlabeled LiDAR scans from past traversals at locations of interest (potentially from other high-end vehicles equipped with LiDAR sensors). Under this setup, we proposed a novel, simple, and end-to-end trainable framework, termed AsyncDepth, to effectively extract relevant features from asynchronous LiDAR traversals of the same location for monocular 3D detectors. We show consistent and significant performance gain (up to 9 AP) across multiple state-of-the-art models and datasets with a negligible additional latency of 9.66 ms and a small storage cost., Comment: Accepted by ICRA 2024. The code can be found at https://github.com/YurongYou/AsyncDepth

Two-stage stochastic programming is a popular framework for optimization under uncertainty, where decision variables are split between first-stage decisions, and second-stage (or recourse) decisions, with the latter being adjusted after uncertainty is realized. These problems are often formulated using Sample Average Approximation (SAA), where uncertainty is modeled as a finite set of scenarios, resulting in a large "monolithic" problem, i.e., where the model is repeated for each scenario. The resulting models can be challenging to solve, and several problem-specific decomposition approaches have been proposed. An alternative approach is to approximate the expected second-stage objective value using a surrogate model, which can then be embedded in the first-stage problem to produce good heuristic solutions. In this work, we propose to instead model the distribution of the second-stage objective, specifically using a quantile neural network. Embedding this distributional approximation enables capturing uncertainty and is not limited to expected-value optimization, e.g., the proposed approach enables optimization of the Conditional Value at Risk (CVaR). We discuss optimization formulations for embedding the quantile neural network and demonstrate the effectiveness of the proposed framework using several computational case studies including a set of mixed-integer optimization problems.

The optimal design of power converters requires accurate knowledge of the dissipation elements of its system to achieve the desired performance and security requirements. Calorimetric methods have surpassed classical electrical methods for the estimation of semiconductor power losses but have mechanical limitations and resort to analytical electrothermal equivalent circuits for this task. These electrothermal models are highly dependent on the topology and technology used on the power converter leading to either simplifications that underestimate the thermal effects or intractable sets of differential equations. To overcome these issues, we propose a novel data-driven identification method to characterize the thermal dynamics of power converters allowing the designer to obtain semiconductor total power losses only by means of temperature measurements without the need of a calorimeter. Given a set of power vs.temperature profiles, our solution identifies the linear model that best fits the data. The solution is based on an optimization problem that allows not only accurate identification but also coding of the desired modeling requirements, such as dynamics' invertibility to allow the estimation of power losses from the temperature profiles. The proposed methodology can be applied to any power converter topology. Furthermore, by obtaining a linear model, standard control theory techniques can be exploited to analyze and control the thermal dynamics. Real experiments validate the generality and accuracy of the proposal.

We show a wedge-decomposable simplicial complex has associated double homology $\mathbb{Z}\oplus\mathbb{Z}$ in bidegrees $(0,0)$, $(-1,4)$.

This paper presents and evaluates a novel method for generating power losses on transistors avoiding high currents. These could heat up the circuit tracks, affecting the accurate thermal modeling of the system. The proposed procedure is based on the transistor current regulation with low gate voltages and the linearity between power and temperature, being useful for all transistor technologies (Si, SiC and GaN). Through this method, low DC currents are enough to bring transistors to their thermal limits. Thermal stability issues and their differences between technologies are discussed and an experimental validation of the method is carried out., Comment: 7 pages, 9 figures

We present the training recipe and results of scaling up PaLI-X, a multilingual vision and language model, both in terms of size of the components and the breadth of its training task mixture. Our model achieves new levels of performance on a wide-range of varied and complex tasks, including multiple image-based captioning and question-answering tasks, image-based document understanding and few-shot (in-context) learning, as well as object detection, video question answering, and video captioning. PaLI-X advances the state-of-the-art on most vision-and-language benchmarks considered (25+ of them). Finally, we observe emerging capabilities, such as complex counting and multilingual object detection, tasks that are not explicitly in the training mix.

Training large, deep neural networks to convergence can be prohibitively expensive. As a result, often only a small selection of popular, dense models are reused across different contexts and tasks. Increasingly, sparsely activated models, which seek to decouple model size from computation costs, are becoming an attractive alternative to dense models. Although more efficient in terms of quality and computation cost, sparse models remain data-hungry and costly to train from scratch in the large scale regime. In this work, we propose sparse upcycling -- a simple way to reuse sunk training costs by initializing a sparsely activated Mixture-of-Experts model from a dense checkpoint. We show that sparsely upcycled T5 Base, Large, and XL language models and Vision Transformer Base and Large models, respectively, significantly outperform their dense counterparts on SuperGLUE and ImageNet, using only ~50% of the initial dense pretraining sunk cost. The upcycled models also outperform sparse models trained from scratch on 100% of the initial dense pretraining computation budget.

The use of machine learning methods helps to improve decision making in different fields. In particular, the idea of bridging predictions (machine learning models) and prescriptions (optimization problems) is gaining attention within the scientific community. One of the main ideas to address this trade-off is the so-called Constraint Learning (CL) methodology, where the structures of the machine learning model can be treated as a set of constraints to be embedded within the optimization problem, establishing the relationship between a direct decision variable $x$ and a response variable $y$. However, most CL approaches have focused on making point predictions for a certain variable, not taking into account the statistical and external uncertainty faced in the modeling process. In this paper, we extend the CL methodology to deal with uncertainty in the response variable $y$. The novel Distributional Constraint Learning (DCL) methodology makes use of a piece-wise linearizable neural network-based model to estimate the parameters of the conditional distribution of $y$ (dependent on decisions $x$ and contextual information), which can be embedded within mixed-integer optimization problems. In particular, we formulate a stochastic optimization problem by sampling random values from the estimated distribution by using a linear set of constraints. In this sense, DCL combines both the high predictive performance of the neural network method and the possibility of generating scenarios to account for uncertainty within a tractable optimization model. The behavior of the proposed methodology is tested in a real-world problem in the context of electricity systems, where a Virtual Power Plant seeks to optimize its operation, subject to different forms of uncertainty, and with price-responsive consumers.

Advances in perception for self-driving cars have accelerated in recent years due to the availability of large-scale datasets, typically collected at specific locations and under nice weather conditions. Yet, to achieve the high safety requirement, these perceptual systems must operate robustly under a wide variety of weather conditions including snow and rain. In this paper, we present a new dataset to enable robust autonomous driving via a novel data collection process - data is repeatedly recorded along a 15 km route under diverse scene (urban, highway, rural, campus), weather (snow, rain, sun), time (day/night), and traffic conditions (pedestrians, cyclists and cars). The dataset includes images and point clouds from cameras and LiDAR sensors, along with high-precision GPS/INS to establish correspondence across routes. The dataset includes road and object annotations using amodal masks to capture partial occlusions and 3D bounding boxes. We demonstrate the uniqueness of this dataset by analyzing the performance of baselines in amodal segmentation of road and objects, depth estimation, and 3D object detection. The repeated routes opens new research directions in object discovery, continual learning, and anomaly detection. Link to Ithaca365: https://ithaca365.mae.cornell.edu/, Comment: Accepted by CVPR 2022

When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables. In this work, we develop a novel Chance Constraint Learning (CCL) methodology with a focus on mixed-integer linear optimization problems which combines ideas from the chance constraint and constraint learning literature. Chance constraints set a probabilistic confidence level for a single or a set of constraints to be fulfilled, whereas the constraint learning methodology aims to model the functional relationship between the problem variables through predictive models. One of the main issues when establishing a learned constraint arises when we need to set further bounds for its response variable: the fulfillment of these is directly related to the accuracy of the predictive model and its probabilistic behaviour. In this sense, CCL makes use of linearizable machine learning models to estimate conditional quantiles of the learned variables, providing a data-driven solution for chance constraints. An open-access software has been developed to be used by practitioners. Furthermore, benefits from CCL have been tested in two real-world case studies, proving how robustness is added to optimal solutions when probabilistic bounds are set for learned constraints.

In day-ahead electricity markets based on uniform marginal pricing, small variations in the offering and bidding curves may substantially modify the resulting market outcomes. In this work, we deal with the problem of finding the optimal offering curve for a risk-averse profit-maximizing generating company (GENCO) in a data-driven context. In particular, a large GENCO's market share may imply that her offering strategy can alter the marginal price formation, which can be used to increase profit. We tackle this problem from a novel perspective. First, we propose a optimization-based methodology to summarize each GENCO's step-wise supply curves into a subset of representative price-energy blocks. Then, the relationship between the market price and the resulting energy block offering prices is modeled through a Bayesian linear regression approach, which also allows us to generate stochastic scenarios for the sensibility of the market towards the GENCO strategy, represented by the regression coefficient probabilistic distributions. Finally, this predictive model is embedded in the stochastic optimization model by employing a constraint learning approach. Results show how allowing the GENCO to deviate from her true marginal costs renders significant changes in her profits and the market marginal price. Furthermore, these results have also been tested in an out-of-sample validation setting, showing how this optimal offering strategy is also effective in a real-world market contest.

This paper focuses on the problem of decentralized pedestrian tracking using a sensor network. Traditional works on pedestrian tracking usually use a centralized framework, which becomes less practical for robotic applications due to limited communication bandwidth. Our paper proposes a communication-efficient, orientation-discriminative feature representation to characterize pedestrian appearance information, that can be shared among sensors. Building upon that representation, our work develops a cross-sensor track association approach to achieve decentralized tracking. Extensive evaluations are conducted on publicly available datasets and results show that our proposed approach leads to improved performance in multi-sensor tracking., Comment: 8 pages, 4 figures, submitted to IEEE/RSJ International Conference on Intelligent Robots and Systems

The interplay between risk aversion and financial derivatives has received increasing attention since the advent of electricity market liberalization. One important challenge in this context is how to develop economically efficient and cost-effective models to integrate renewable energy sources (RES) in the electricity market, which constitutes a relatively new and exciting field of research. This paper proposes a game-theoretical equilibrium model that characterizes the interactions between oligopolistic generators in a two-stage electricity market under the presence of high RES penetration. Given conventional generators with generation cost uncertainty and renewable generators with intermittent and stochastic capacity, we consider a single futures contract market that is cleared prior to a spot market where the energy delivery takes place. We introduce physical and financial contracts to evaluate their performance assess their impact on the electricity market outcomes and examine how these depend on the level of RES penetration. Since market participants are usually risk-averse, a coherent risk measure is introduced to deal with both risk-neutral and risk-averse generators. We derive analytical relationships between contracts, study the implications of uncertainties, test the performance of the proposed equilibrium model and its main properties through numerical examples. Our results show that overall electricity prices, generation costs, profits, and quantities for conventional generators decrease, whereas quantities and profits for RES generators increase with RES penetration. Hence, both physical and financial contracts efficiently mitigate the impact of uncertainties and help the integration of RES into the electricity system.

Machine learning models based on the aggregated outputs of submodels, either at the activation or prediction levels, often exhibit strong performance compared to individual models. We study the interplay of two popular classes of such models: ensembles of neural networks and sparse mixture of experts (sparse MoEs). First, we show that the two approaches have complementary features whose combination is beneficial. This includes a comprehensive evaluation of sparse MoEs in uncertainty related benchmarks. Then, we present Efficient Ensemble of Experts (E$^3$), a scalable and simple ensemble of sparse MoEs that takes the best of both classes of models, while using up to 45% fewer FLOPs than a deep ensemble. Extensive experiments demonstrate the accuracy, log-likelihood, few-shot learning, robustness, and uncertainty improvements of E$^3$ over several challenging vision Transformer-based baselines. E$^3$ not only preserves its efficiency while scaling to models with up to 2.7B parameters, but also provides better predictive performance and uncertainty estimates for larger models., Comment: 59 pages, 26 figures, 36 tables. Accepted at TMLR

In the present work we tackle the problem of finding the optimal price tariff to be set by a risk-averse electric retailer participating in the pool and whose customers are price-sensitive. We assume that the retailer has access to a sufficiently large smart-meter dataset from which it can statistically characterize the relationship between the tariff price and the demand load of its clients. Three different models are analyzed to predict the aggregated load as a function of the electricity prices and other parameters, as humidity or temperature. More specifically, we train linear regression (predictive) models to forecast the resulting demand load as a function of the retail price. Then we will insert this model in a quadratic optimization problem which evaluates the optimal price to be offered. This optimization problem accounts for different sources of uncertainty including consumer's response, pool prices and renewable source availability, and relies on a stochastic and risk-averse formulation. In particular, one important contribution of this work is to base the scenario generation and reduction procedure on the statistical properties of the resulting predictive model. This allows us to properly quantify (data-driven) not only the expected value but the level of uncertainty associated with the main problem parameters. Moreover, we consider both standard forward based contracts and the recently introduced power purchase agreement contracts as risk-hedging tools for the retailer. The results are promising as profits are found for the retailer with highly competitive prices and some possible improvements are shown if richer datasets could be available in the future. A realistic case study and multiple sensitivity analyses have been performed to characterize the risk-aversion behavior of the retailer considering price-sensitive consumers.

The paper develops a typical management problem of a large power producer (i.e., he can partly influence the market price). In particular, he routinely needs to decide how much of his generation it is preferable to commit to fixed price bilateral contracts (e.g., futures) or to the spot market. However, he also needs to plan how to distribute the production across the different plants under his control. The two decisions, namely the sales-mix and the generation plan, naturally interact, since the opportunity to influence the spot price depends, among other things, by the amount of the energy that the producer directs on the spot market. We develop a risk management problem, since we consider an optimization problem combining a trade-off between expectation and conditional value at risk of the profit function of the producer. The sources of uncertainty are relatively large and encompass demand, renewables generation and the fuel costs of conventional plants. We also model endogenously the price of futures in a way reflecting an information advantage of a large power producer. In particular, it is assumed that the market forecast the price of futures in a naive way, namely not anticipating the impact of the large producer on the spot market. The paper provides a MILP formulation of the problem, and it analyzes the solution through a simulation based on Spanish power market data.

Demand response (DR) programs play a crucial role in improving system reliability and mitigating price volatility by altering the core profile of electricity consumption. This paper proposes a game-theoretical model that captures the dynamic interplay between retailers (leaders) and consumers (followers) in a tariffs-based electricity market under uncertainty. The proposed procedure offers theoretical and economic insights by analyzing demand flexibility within a hierarchical decision-making framework. In particular, two main market configurations are examined under uncertainty: i) there exists a retailer that exercises market power over consumers, and ii) the retailer and the consumers participate in a perfect competitive game. The former case is formulated as a mathematical program with equilibrium constraints (MPEC), whereas the latter case is recast as a mixed-integer linear program (MILP). These problems are solved by deriving equivalent tractable reformulations based on the Karush-Kuhn-Tucker (KKT) optimality conditions of each agent's problem. Numerical simulations based on real data from the European Energy Exchange platform are used to illustrate the performance of the proposed methodology. The results indicate that the proposed model effectively characterizes the interactions between retailers and flexible consumers in both perfect and imperfect market structures. Under perfect competition, the economic benefits extend not only to consumers but also to overall social welfare. Conversely, in an imperfect market, retailers leverage consumer flexibility to enhance their expected profits, transferring the risk of uncertainty to end-users. Additionally, the degree of consumer flexibility and their valuation of electricity consumption play significant roles in shaping market outcomes., Comment: 32

The European Union Emission Trading Scheme (EU ETS) is a cornerstone of the EU's strategy to fight climate change and an important device for plummeting greenhouse gas (GHG) emissions in an economically efficient manner. The power industry has switched to an auction-based allocation system at the onset of Phase III of the EU ETS to bring economic efficiency by negating windfall profits that have been resulted from grandfathered allocation of allowances in the previous phases. In this work, we analyze and simulate the interaction of oligopolistic generators in an electricity market with a game-theoretical framework where the electricity and the emissions markets interact in a two-stage electricity market. For analytical simplicity, we assume a single futures market where the electricity is committed at the futures price, and the emissions allowance is contracted in advance, prior to a spot market where the energy and allowances delivery takes place. Moreover, a coherent risk measure is applied (Conditional Value at Risk) to model both risk averse and risk neutral generators and a two-stage stochastic optimization setting is introduced to deal with the uncertainty of renewable capacity, demand, generation, and emission costs. The performance of the proposed equilibrium model and its main properties are examined through realistic numerical simulations. Our results show that renewable generators are surging and substituting conventional generators without compromising social welfare. Hence, both renewable deployment and emission allowance auctioning are effectively reducing GHG emissions and promoting low-carbon economic path., Comment: 31 Pages, 8 figures, Accepted paper (Energy Economics, 2018)