Neural Information Processing Systems http://nips.cc/

Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex physical systems described by parametrized PDEs, by nonlinearly compressing the solution manifold into a handful of latent coordinates. Until now, design and application of DL-ROMs mainly focused on physically parameterized problems. Within this work, we provide a novel extension of these architectures to problems featuring geometrical variability and parametrized domains, namely, we propose Continuous Geometry-Aware DL-ROMs (CGA-DL-ROMs). In particular, the space-continuous nature of the proposed architecture matches the need to deal with multi-resolution datasets, which are quite common in the case of geometrically parametrized problems. Moreover, CGA-DL-ROMs are endowed with a strong inductive bias that makes them aware of geometrical parametrizations, thus enhancing both the compression capability and the overall performance of the architecture. Within this work, we justify our findings through a thorough theoretical analysis, and we practically validate our claims by means of a series of numerical tests encompassing physically-and-geometrically parametrized PDEs, ranging from the unsteady Navier-Stokes equations for fluid dynamics to advection-diffusion-reaction equations for mathematical biology.

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic interpretation in the number n of datapoints, which allows us to study EP's convergence with respect to the true posterior.

Estimation-of-distribution algorithms (EDAs) are optimization algorithms that learn a distribution on the search space from which good solutions can be sampled easily. A key parameter of most EDAs is the sample size (population size). If the population size is too small, the update of the probabilistic model builds on few samples, leading to the undesired effect of genetic drift. Too large population sizes avoid genetic drift, but slow down the process. Building on a recent quantitative analysis of how the population size leads to genetic drift, we design a smart-restart mechanism for EDAs. By stopping runs when the risk for genetic drift is high, it automatically runs the EDA in good parameter regimes. Via a mathematical runtime analysis, we prove a general performance guarantee for this smart-restart scheme. This in particular shows that in many situations where the optimal (problem-specific) parameter values are known, the restart scheme automatically finds these, leading to the asymptotically optimal performance. We also conduct an extensive experimental analysis. On four classic benchmark problems, we clearly observe the critical influence of the population size on the performance, and we find that the smart-restart scheme leads to a performance close to the one obtainable with optimal parameter values. Our results also show that previous theory-based suggestions for the optimal population size can be far from the optimal ones, leading to a performance clearly inferior to the one obtained via the smart-restart scheme. We also conduct experiments with PBIL (cross-entropy algorithm) on two combinatorial optimization problems from the literature, the max-cut problem and the bipartition problem. Again, we observe that the smart-restart mechanism finds much better values for the population size than those suggested in the literature, leading to a much better performance.

Many real-world applications have the time-linkage property, and the only theoretical analysis is recently given by Zheng, et al. (TEVC 2021) on their proposed time-linkage OneMax problem, OneMax$_{(0,1^n)}$. However, only two elitist algorithms (1+1)EA and ($\mu$+1)EA are analyzed, and it is unknown whether the non-elitism mechanism could help to escape the local optima existed in OneMax$_{(0,1^n)}$. In general, there are few theoretical results on the benefits of the non-elitism in evolutionary algorithms. In this work, we analyze on the influence of the non-elitism via comparing the performance of the elitist (1+$\lambda$)EA and its non-elitist counterpart (1,$\lambda$)EA. We prove that with probability $1-o(1)$ (1+$\lambda$)EA will get stuck in the local optima and cannot find the global optimum, but with probability $1$, (1,$\lambda$)EA can reach the global optimum and its expected runtime is $O(n^{3+c}\log n)$ with $\lambda=c \log_{\frac{e}{e-1}} n$ for the constant $c\ge 1$. Noting that a smaller offspring size is helpful for escaping from the local optima, we further resort to the compact genetic algorithm where only two individuals are sampled to update the probabilistic model, and prove its expected runtime of $O(n^3\log n)$. Our computational experiments also verify the efficiency of the two non-elitist algorithms.

Today, predictive models help many companies run their business-critical processes. These predictive models are probabilistic -- they involve chance variation -- and they depend on some underlying assumptions to make them work properly. Chief among these are 1.) that the data flowing into them is distributed in a certain way and 2.) that underlying business scenarios are unchanged from the time the models were created. As a result, it's important for companies to monitor changes to business scenarios and data quality, otherwise the model will no longer perform as intended. Additionally, it's important that these models comply with applicable laws and regulations once they are in production (active use).

One of the key difficulties in using estimation-of-distribution algorithms is choosing the population sizes appropriately: Too small values lead to genetic drift, which can cause enormous difficulties. In the regime with no genetic drift, however, often the runtime is roughly proportional to the population size, which renders large population sizes inefficient. Based on a recent quantitative analysis which population sizes lead to genetic drift, we propose a parameter-less version of the compact genetic algorithm that automatically finds a suitable population size without spending too much time in situations unfavorable due to genetic drift. We prove an easy mathematical runtime guarantee for this algorithm and conduct an extensive experimental analysis on four classic benchmark problems. The former shows that under a natural assumption, our algorithm has a performance similar to the one obtainable from the best population size. The latter confirms that missing the right population size can be highly detrimental and shows that our algorithm as well as a previously proposed parameter-less one based on parallel runs avoids such pitfalls. Comparing the two approaches, ours profits from its ability to abort runs which are likely to be stuck in a genetic drift situation.

Researchers at the University of North Carolina's Center for Geospatial Analytics (CGA) are using artificial intelligence (AI) and machine learning (ML) to help farmers better adapt their crops to changing climates. Speaking to ZDNet, CGA associate director Ranga Raju Vatsavai said his team of researchers has been working in partnership with Lenovo for the last two years to develop AI and ML solutions to help farmers preemptively identify ways to best optimise water and energy -- and ultimately address the threats to food insecurity. "Our area of research is to extract actionable knowledge from the datasets. Food, energy, and water are a good application because the population is going to reach 10 billion by 2050. Right now, we are utilising 70% of fresh water for agriculture," he said.

In the first runtime analysis of an estimation-of-distribution algorithm (EDA) on the multi-modal jump function class, Hasen\"ohrl and Sutton (GECCO 2018) proved that the runtime of the compact genetic algorithm with suitable parameter choice on jump functions with high probability is at most polynomial (in the dimension) if the jump size is at most logarithmic (in the dimension), and is at most exponential in the jump size if the jump size is super-logarithmic. The exponential runtime guarantee was achieved with a hypothetical population size that is also exponential in the jump size. Consequently, this setting cannot lead to a better runtime. In this work, we show that any choice of the hypothetical population size leads to a runtime that, with high probability, is at least exponential in the jump size. This result might be the first non-trivial exponential lower bound for EDAs that holds for arbitrary parameter settings.