Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators—trained using model simulations—to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin–Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics.

Predicting how species diversity changes along environmental gradients is an enduring problem in ecology. In microbes, current theories tend to invoke energy availability and enzyme kinetics as the main drivers of temperature-richness relationships. Here, we derive a general empirically-grounded theory that can explain this phenomenon by linking microbial species richness in competitive communities to variation in the temperature-dependence of their interaction and growth rates. Specifically, the shape of the microbial community temperature-richness relationship depends on how rapidly the strength of effective competition between species pairs changes with temperature relative to the variance of their growth rates. Furthermore, it predicts that a thermal specialist-generalist tradeoff in growth rates alters coexistence by shifting this balance, causing richness to peak at relatively higher temperatures. Finally, we show that the observed patterns of variation in thermal performance curves of metabolic traits across extant bacterial taxa is indeed sufficient to generate the variety of community-level temperature-richness responses observed in the real world. Our results provide a new and general mechanism that can help explain temperature-diversity gradients in microbial communities, and provide a quantitative framework for interlinking variation in the thermal physiology of microbial species to their community-level diversity.