We study the subclass of potential mean-field games in which the running interaction cost and the terminal target cost are both expressed through reproducing-kernel maximum mean discrepancy (MMD) penalties, and develop a computational framework that exploits this kernel structure. Both costs are estimated from finite-sample empirical distributions using a random Fourier U-statistic representation that is unbiased and has linear cost in the batch size. The drift of the controlled diffusion is parametrized by a neural network and trained via stochastic gradient descent. For this subclass we prove a sample-level almost-sure convergence theorem and an explicit almost-sure rate of convergence, under coupled rate conditions on the penalty parameter, the random-feature count, the sample size, and the optimization tolerance. The framework includes the kernel-MMD-penalty Schrödinger bridge problem as the special case of a vanishing interaction cost. Numerical experiments illustrate the method on the Schrödinger bridge problem in dimensions up to one hundred, and on an electric vehicle charging coordination problem with per-vehicle physical heterogeneity, where an aggregate-demand congestion cost represents price-feedback competition at the population level and the terminal MMD penalty shapes the state-of-charge distribution at the deadline.

The use of residential photovoltaics has increased dramatically in recent years. With battery systems becoming more affordable, the optimal operation of a photovoltaic-battery system can bring significant savings to households. Optimal control requires correct forecasts of underlying parameters, such as photovoltaic power generation, to schedule the battery. While forecasting models have become increasingly accurate due to algorithmic advances and data availability, accuracy is typically measured in generic metrics which might not align with the downstream application. This study proposes a decision-focused learning framework that integrates optimization and prediction by training a Long Short-Term Memory photovoltaic energy forecaster on the downstream optimal scheduling of a battery system. The proposed methodology is compared against a standard two-phase approach. Across a 14-month evaluation period, the decision-focused method reduced average electricity costs across twenty buildings by 3.6% when normalized against performance bounds defined by a perfect forecast and a baseline of no optimization. Critically, this financial improvement was achieved despite the model exhibiting a root mean squared error of 19.9%, significantly higher than the decoupled model's 8.2%. Warm-starting the decision-focused model further improves results, lowering average cost by approximately 8%, while also mitigating the negative impact on statistical accuracy (root mean squared error of 13.7%). The findings are statistically significant at the 0.001 level across the twenty households and for each household individually. These results demonstrate that aligning forecast models with optimization goals is key for achieving cost advantages in PV-battery systems. Future research should replicate these findings on other datasets, alternate forecasting models and alternate optimization algorithms.

Ford and GM are backing away from electric vehicles and moving into the battery storage business. And it all comes back to AI. Automakers make cars--it's in the name. But lately, politics, current events, and Wall Street's latest preoccupation, artificial intelligence, have them looking a lot more like energy companies. The pivot, analysts say, could give US auto manufacturers struggling through a transition to electric vehicles an easier path over the next few years. Whether it works will come down to the same technology that automakers once promised would power the majority of their lineups: batteries .

SoftBank will partner with South Korea's Cosmos Lab and DeltaX to enable mass production of large-scale battery cells from the fiscal year starting next April. SoftBank Group's mobile unit said it plans to begin large-scale battery cell manufacturing at its plant in Sakai, Osaka Prefecture, to address growing power demand for AI services. SoftBank Corp. will partner with South Korea's Cosmos Lab and DeltaX to enable mass production from the fiscal year starting next April, the company said in a statement Monday. The aim is to output energy storage systems at a scale of one gigawatt-hour per year, SoftBank said, which would make it one of the largest facilities in Japan, according to data from BloombergNEF. SoftBank could scale up to a capacity of several GWh, Bloomberg reported last month.

Send the pool guy packing. One of these robotic buddies can maintain your water quality instead. Cleaning swimming pools is not fun. I learned this simple logic as a kid growing up in and around pools--it's the only way to survive summer in Houston, Texas. Four years ago, I became a pool owner myself, and I found that the rule still holds. Jumping into the pool on a hot day remains a rare treat, but if the pool is filled with leaves and dirt, that treat becomes a lot less delightful. And when the thermometer is reading over 100 degrees Fahrenheit, the thought of laboring on the pool deck, scooping out debris with a net, is downright cruel.

Will fusion power get cheap? New research suggests that cost declines could be slow for the technology. Fusion power could provide a steady, zero-emissions source of electricity in the future--if companies can get plants built and running. But a new study suggests that even if that future arrives, it might not come cheap. Technologies tend to get less expensive over time. Lithium-ion batteries are now about 90% cheaper than they were in 2013.

The Download: Early adopters cash in on China's OpenClaw craze, and US batteries slump Hustlers are cashing in on China's OpenClaw AI craze In January, Beijing-based software engineer Feng Qingyang started tinkering with OpenClaw, a new AI tool that can take over a device and autonomously complete tasks. Within weeks, he was advertising "OpenClaw installation support" on a second-hand shopping site. Today, his side gig is a fully-fledged business with over 100 employees and 7,000 completed orders. Feng is among a small cohort of savvy early adopters making serious cash from China's OpenClaw craze. As users with little technical background want in, a cottage industry of installation services and preconfigured hardware has sprung up. The rise of these tinkerers shows just how eager the general public in China is to adopt cutting-edge AI--despite huge security risks.

The souped-up G-Wiz EV has a range of 18 miles and topped 40 miles per hour. The G-Wiz, one of the earlier electric vehicles, technically seats four passengers. Breakthroughs, discoveries, and DIY tips sent six days a week. Anyone who's walked through the grounds of a music festival or even peeked into a public trash bin has likely noticed a deluge of discarded, single-use nicotine vapes. These vapes have surged in popularity, with the United Nations estimating at least 844 million of them were discarded by 2022 alone .

The inkless device works a bit like a printing press. Breakthroughs, discoveries, and DIY tips sent six days a week. Lego kits have become impressively intricate over the years, but the company really outdid itself with a 2079-piece typewriter in 2021. Part of its Ideas series, the brickmakers released the fully functioning mechanical keyboard. It's a unique and extremely well designed set, although not without its limits.