Consider a supercomputer so fast and powerful that it generates simulated models to better understand everything from irregular human heartbeats to earthquakes. Picture tiny brain implants that can restore sight and possibly memory. Or what about the world's largest laser, with powerful beams, zooming rocket-like across three football fields—research that could lead to future sources of clean energy?

This is the world inside the Lawrence Livermore National Laboratory, a national security lab 50 miles east of San Francisco.

National labs have been around for decades and are commonly associated with nuclear weapons testing. But inside Livermore's mile-square campus, some 6,000 employees hover over hundreds of projects that span multiple industries, including oil and gas, health care and transportation.

Livermore, like other labs, often collaborates with private companies to create solutions such as more fuel-efficient, long-haul trucks, and more resilient airplane components. The lab secured $1.5 billion in funding from multiple sources last year—the majority from the government.

But in recent years, companies have been ponying up more money. Private industry contributed about $40 million for research at Livermore in 2013. "That will continue to go up," said Richard Rankin, director of the lab's industrial partnerships office.

Labs also are emphasizing they're open to collaboration. And part of the courtship can be explained by the growing complexity of modern problems. Think cyber and chemical warfare, or securing future energy supplies as climate change barrels down, or treating and managing more American soldiers, returning injured without limbs.

Just as major energy companies have worked together to drill ever deeper for offshore oil, leading government-funded labs and companies are realizing they can't go it alone.

As the world becomes a scarier place, competition also is growing for brain power to solve the most pressing problems. In Silicon Valley, for example, a top science degree means options—research labs of your choosing, maybe an Apple gig, maybe a founding role at a start-up.

But globally, there's also demand for talent and big ideas—an innovation arms race, if you will.

Lawrence Livermore has the world's third-fastest supercomputer with the help of IBM. But China now holds the number one slot. And while the Livermore Lab has the world's largest laser, France, China and Russia are pursuing super lasers of their own.

Don't laugh at this "mine is bigger, better, faster" game. Initial breakthroughs in science and technology can lead to patent-related revenues, of course. But first-mover advantages can also help secure medicine such as a cancer treatment or an Ebola vaccine. And there are national security consequences to such information. Just recall the 2011 film "Contagion" and the loss of social order, as a coveted vaccine is administered. You can see how this stuff might play out.