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Simulating mantle convection often requires reaching a computationally expensive steady-state, crucial for deriving scaling laws for thermal and dynamical flow properties and benchmarking numerical solutions. The strong temperature dependence of the rheology of mantle rocks causes viscosity variations of several orders of magnitude, leading to a slow-evolving stagnant lid where heat conduction dominates, overlying a rapidly-evolving and strongly convecting region. Time-stepping methods, while effective for fluids with constant viscosity, are hindered by the Courant criterion, which restricts the time step based on the system's maximum velocity and grid size. Consequently, achieving steady-state requires a large number of time steps due to the disparate time scales governing the stagnant and convecting regions. We present a concept for accelerating mantle convection simulations using machine learning. We generate a dataset of 128 two-dimensional simulations with mixed basal and internal heating, and pressure- and temperature-dependent viscosity. We train a feedforward neural network on 97 simulations to predict steady-state temperature profiles. These can then be used to initialize numerical time stepping methods for different simulation parameters. Compared to typical initializations, the number of time steps required to reach steady-state is reduced by a median factor of 3.75. The benefit of this method lies in requiring very few simulations to train on, providing a solution with no prediction error as we initialize a numerical method, and posing minimal computational overhead at inference time. We demonstrate the effectiveness of our approach and discuss the potential implications for accelerated simulations for advancing mantle convection research.

Cloud microphysics has important consequences for climate and weather phenomena, and inaccurate representations can limit forecast accuracy. While atmospheric models increasingly resolve storms and clouds, the accuracy of the underlying microphysics remains limited by computationally expedient bulk moment schemes based on simplifying assumptions. Droplet-based Lagrangian schemes are more accurate but are underutilized due to their large computational overhead. Machine learning (ML) based schemes can bridge this gap by learning from vast droplet-based simulation datasets, but have so far struggled to match the accuracy and stability of bulk moment schemes. To address this challenge, we developed SuperdropNet, an ML-based emulator of the Lagrangian superdroplet simulations. To improve accuracy and stability, we employ multi-step autoregressive prediction during training, impose physical constraints, and carefully control stochasticity in the training data. Superdropnet predicted hydrometeor states and cloud-to-rain transition times more accurately than previous ML emulators, and matched or outperformed bulk moment schemes in many cases. We further carried out detailed analyses to reveal how multistep autoregressive training improves performance, and how the performance of SuperdropNet and other microphysical schemes hydrometeors' mass, number and size distribution. Together our results suggest that ML models can effectively emulate cloud microphysics, in a manner consistent with droplet-based simulations.

Simulation-based inference (SBI) refers to statistical inference on stochastic models for which we can generate samples, but not compute likelihoods. Like SBI algorithms, generative adversarial networks (GANs) do not require explicit likelihoods. We study the relationship between SBI and GANs, and introduce GATSBI, an adversarial approach to SBI. GATSBI reformulates the variational objective in an adversarial setting to learn implicit posterior distributions. Inference with GATSBI is amortised across observations, works in high-dimensional posterior spaces and supports implicit priors. We evaluate GATSBI on two SBI benchmark problems and on two high-dimensional simulators. On a model for wave propagation on the surface of a shallow water body, we show that GATSBI can return well-calibrated posterior estimates even in high dimensions. On a model of camera optics, it infers a high-dimensional posterior given an implicit prior, and performs better than a state-of-the-art SBI approach. We also show how GATSBI can be extended to perform sequential posterior estimation to focus on individual observations. Overall, GATSBI opens up opportunities for leveraging advances in GANs to perform Bayesian inference on high-dimensional simulation-based models.

This report summarizes the long-term findings of a rigorous random assignment evaluation of the WorkAdvance model, a sectoral training and advancement initiative. Launched in 2011, WorkAdvance goes beyond the previous generation of employment programs by introducing demand-driven skills training and a focus on jobs that have identifiable career pathways. The model is heavily influenced by the positive findings from the Sectoral Employment Impact Study completed in 2010, as well as prior research on job retention and career advancement strategies. The WorkAdvance model was implemented between June 2011 and June 2013 by four providers -- Per Scholas, St. Nicks Alliance, Madison Strategies Group, and Towards Employment -- and a total of 2,564 individuals enrolled in the study. Several previous reports described the implementation, participation, cost, and interim impact findings of WorkAdvance and showed encouraging evidence for the WorkAdvance model. The impact findings presented in those reports covered the first three years of follow-up. While those findings showed earnings gains for some programs in some years, whether WorkAdvance could consistently increase earnings in the long term was still an open question. This report presents the long-term economic impacts of WorkAdvance and covers a two-year period occurring between four and eight years after individuals entered the study. The economic outcomes are based on National Directory of New Hires data and include 2017 and 2018. The report also builds on a previous cost analysis and presents findings from a full benefit-cost analysis to examine whether the effects of WorkAdvance resulted in gains or losses from the perspective of WorkAdvance participants, the government, and society. Key Findings: (1) The WorkAdvance program at Per Scholas increased average earnings in 2017 and 2018; there were no statistically significant effects on average earnings at the other three sites. There is evidence that some of the WorkAdvance programs increased the likelihood of individuals having earnings of at least $30,000 in some time periods. None of the WorkAdvance sites increased employment by a statistically significant amount in either long-term follow-up year; (2) In the pooled sample from all four providers, WorkAdvance had no effect on employment but increased average earnings and the likelihood of individuals having high earnings; (3) The overall pattern of economic impact findings suggests that the earnings-based impacts are driven by WorkAdvance group members having higher wages than control group members, rather than by being employed at a higher rate. This suggests WorkAdvance group members are advancing over time, as intended by the WorkAdvance model; and (4) The findings from the benefit-cost analysis are positive from the perspectives of the participants, the government, and society at all four sites. Overall, the WorkAdvance results support the case for focusing on how sector programs can be improved. The long-term economic impacts show that sector programs can increase earnings in the longer term and can lead to advancement gains over time for low-income individuals, but not all sector programs will lead to increases in employment and earnings. Focusing future efforts on how to make the sectoral approach -- in particular, the advancement-focused services -- more consistently successful can help workforce providers strengthen sector-based programs. This is the final planned report for the WorkAdvance evaluation.

Using a lifecycle framework with Epstein-Zin (1989) utility and a mixed-integer optimization approach, we compute the optimal age to claim Social Security benefits. Taking advantage of homogeneity, a sufficient statistic is the ratio of wealth to the primary insurance amount (PIA). If the investor's wealth to PIA ratio exceeds a certain threshold, individuals should defer Social Security for at least a year. The optimal threshold depends on mortality assumptions and an individual's utility preferences, but is less sensitive to capital market assumptions. The threshold wealth to PIA ratio increases from 5.5 for men and 5.2 for women at age 62 to 11.1 for men and 10.4 for women at age 69. Below the threshold wealth to PIA ratio, individuals claim Social Security to raise consumption. Above this level, investors can afford to fund consumption out of wealth for at least one year, and then claim a higher benefit.

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for such 'likelihood-free' algorithms has been lacking. This has made it difficult to compare algorithms and identify their strengths and weaknesses. We set out to fill this gap: We provide a benchmark with inference tasks and suitable performance metrics, with an initial selection of algorithms including recent approaches employing neural networks and classical Approximate Bayesian Computation methods. We found that the choice of performance metric is critical, that even state-of-the-art algorithms have substantial room for improvement, and that sequential estimation improves sample efficiency. Neural network-based approaches generally exhibit better performance, but there is no uniformly best algorithm. We provide practical advice and highlight the potential of the benchmark to diagnose problems and improve algorithms. The results can be explored interactively on a companion website. All code is open source, making it possible to contribute further benchmark tasks and inference algorithms., Comment: In AISTATS 2021

Scientists and engineers employ stochastic numerical simulators to model empirically observed phenomena. In contrast to purely statistical models, simulators express scientific principles that provide powerful inductive biases, improve generalization to new data or scenarios and allow for fewer, more interpretable and domain-relevant parameters. Despite these advantages, tuning a simulator's parameters so that its outputs match data is challenging. Simulation-based inference (SBI) seeks to identify parameter sets that a) are compatible with prior knowledge and b) match empirical observations. Importantly, SBI does not seek to recover a single 'best' data-compatible parameter set, but rather to identify all high probability regions of parameter space that explain observed data, and thereby to quantify parameter uncertainty. In Bayesian terminology, SBI aims to retrieve the posterior distribution over the parameters of interest. In contrast to conventional Bayesian inference, SBI is also applicable when one can run model simulations, but no formula or algorithm exists for evaluating the probability of data given parameters, i.e. the likelihood. We present $\texttt{sbi}$, a PyTorch-based package that implements SBI algorithms based on neural networks. $\texttt{sbi}$ facilitates inference on black-box simulators for practising scientists and engineers by providing a unified interface to state-of-the-art algorithms together with documentation and tutorials., Comment: Alvaro Tejero-Cantero, Jan Boelts, Michael Deistler, Jan-Matthis Lueckmann and Conor Durkan contributed equally in shared first authorship. This manuscript has been submitted for consideration to the Journal of Open Source Software (JOSS). 4 pages, no figures; v2: added link to sbi home

How can one perform Bayesian inference on stochastic simulators with intractable likelihoods? A recent approach is to learn the posterior from adaptively proposed simulations using neural network-based conditional density estimators. However, existing methods are limited to a narrow range of proposal distributions or require importance weighting that can limit performance in practice. Here we present automatic posterior transformation (APT), a new sequential neural posterior estimation method for simulation-based inference. APT can modify the posterior estimate using arbitrary, dynamically updated proposals, and is compatible with powerful flow-based density estimators. It is more flexible, scalable and efficient than previous simulation-based inference techniques. APT can operate directly on high-dimensional time series and image data, opening up new applications for likelihood-free inference.

This brief is the third in a series documenting the implementation of an economic mobility initiative supported by New York City's Change Capital Fund (CCF). CCF is a consortium of New York City donors formed to invest in local nonprofits that undertake data-driven antipoverty strategies integrating housing, education, and employment services. CCF donors believe that an integrated approach to service delivery is an important way to "saturate" areas of persistent poverty with intensive, comprehensive services, cultivating multiple pathways toward neighborhood-level change. The first brief described CCF in detail; introduced the initiative's first grantees, located in Brooklyn and the Bronx; and shared the organizations' ambitious work plans and start-up efforts. The second brief describes two pervasive challenges to service coordination and the ways grantees have responded to them. [For the first brief in this series, "The Promise of a Community-Based Approach to Economic Opportunity: New York City's Change Capital Fund. No. 1," see ED570529. For the second brief in this series, "Addressing Challenges in Community-Based Service Coordination: Breaking Down Silos to Promote Economic Opportunity. New York City's Change Capital Fund. No. 2," see ED570521.]