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Replica exchange stochastic gradient Langevin dynamics (reSGLD) is an effective sampler for non-convex learning in large-scale datasets. However, the simulation may encounter stagnation issues when the high-temperature chain delves too deeply into the distribution tails. To tackle this issue, we propose reflected reSGLD (r2SGLD): an algorithm tailored for constrained non-convex exploration by utilizing reflection steps within a bounded domain. Theoretically, we observe that reducing the diameter of the domain enhances mixing rates, exhibiting a quadratic behavior. Empirically, we test its performance through extensive experiments, including identifying dynamical systems with physical constraints, simulations of constrained multi-modal distributions, and image classification tasks. The theoretical and empirical findings highlight the crucial role of constrained exploration in improving the simulation efficiency. 

We propose a federated averaging Langevin algorithm (FA-LD) for uncertainty quantification and mean predictions with distributed clients. In particular, we generalize beyond normal posterior distributions and consider a general class of models. We develop theoretical guarantees for FA-LD for strongly log-concave distributions with non-i.i.d data and study how the injected noise and the stochastic-gradient noise, the heterogeneity of data, and the varying learning rates affect the convergence. Such an analysis sheds light on the optimal choice of local updates to minimize the communication cost. Important to our approach is that the communication efficiency does not deteriorate with the injected noise in the Langevin algorithms. In addition, we examine in our FA-LD algorithm both independent and correlated noise used over different clients. We observe that there is a trade-off between the pairs among communication, accuracy, and data privacy. As local devices may become inactive in federated networks, we also show convergence results based on different averaging schemes where only partial device updates are available. In such a case, we discover an additional bias that does not decay to zero. 

Most marine gas hydrate systems follow a vertical pattern with hydrate overlying free gas. Here we document the discovery of a gas to hydrate system in a horizontal sand layer in the Qiongdongnan Basin of the South China Sea. Eight wells were drilled by the Guangzhou Marine Geological Survey in 2021–2022 to investigate the occurrence and mechanisms responsible for the formation of the system. We describe a free gas‐bearing sand reservoir at the center of the system sustained by advecting hot fluids and gas; away from the advecting zone, the cooler, surrounding sand reservoir is filled with hydrate. Observations at this site show that advective heat has a large control on hydrate formation in sands and may be a key mechanism which allows gas migration within the hydrate stability zone and the formation of high‐saturation hydrate in sand layers.

 

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from quadratic to linear given the sufficiently many chains. However, such an innovation largely disappears in big data due to the limited chains and few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote non-reversibility and propose a few solutions to tackle the underlying bias caused by the geometric stopping time. Notably, in big data scenarios, we obtain a nearly linear communication cost based on the optimal window size. In addition, we also adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct approximation tasks for complex posteriors without much tuning costs.

 

Parallel tempering (PT), also known as replica exchange, is the go-to workhorse for simulations of multi-modal distributions. The key to the success of PT is to adopt efficient swap schemes. The popular deterministic even-odd (DEO) scheme exploits the non-reversibility property and has successfully reduced the communication cost from O(P 2) to O(P) given sufficient many P chains. However, such an innovation largely disappears in big data problems due to the limited chains and extremely few bias-corrected swaps. To handle this issue, we generalize the DEO scheme to promote the non-reversibility and obtain an appealing communication cost O(P log P) based on the optimal window size. In addition, we also analyze the bias when we adopt stochastic gradient descent (SGD) with large and constant learning rates as exploration kernels. Such a user-friendly nature enables us to conduct large-scale uncertainty approximation tasks without much tuning costs.