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.
Read MoreWhy are American pigs dying?
This push to innovate or embrace the "art of the possible," as one scientist put it, is why websites track the supercomputer race, which China is winning at the moment. "We should be concerned about that," said Frederick Streitz, director of the lab's High Performance Computing Innovation Center.
Added Streitz: "Ideas are power."
Livermore was founded in 1952, during the height of the Cold War, to tackle national security challenges through science, engineering and technology.
It was a formal naval base, and squat barracks remain on the property. Pilots in training were dunked into a swimming pool.
The lab feels like a college campus or tech company. Cyclists take a break from research, likely pedaling past one of the many wineries in the Tri-Valley.
Beyond the region, Livermore is among other leading national labs including Los Alamos in New Mexico and Oak Ridge in Tennessee.
The groundwork for the government and private company collaboration was laid by passage of the Federal Technology Transfer Act in 1986. In industry circles, it's widely referred to as "tech transfer." And the shift is only intensifying,
Government-funded U.S. science labs receive about $140 billion annually in taxpayer money. But even the most gee-whiz research is just that: research. Every federal dollar spent creating early-stage inventions in the lab requires $10 of private sector-funded development to generate a useful product.
Plus, there's no guaranteed return. Nailing a commercial solution or patent, after months or years of research, can be akin to winning the lottery. The stakes, meanwhile, for successful research only are getting higher.
Beyond the growing intricacy of scientific problems, there's a public perception that taxpayer-funded research should yield concrete results. This expectation emerged during the 1980s recession and has intensified in recent years, said Joe Allen, who helped create and pass the technology transfer legislation.
"Virtually every government is saying that publicly funded research needs to be made into a practical benefit for its taxpayers," said Allen, now president of Allen & Associates, based in Bethesda, Ohio. The firm specializes in managing public-private partnerships.
Added Allen: "When taxpayers fund cutting-edge research, they expect more than a white paper. They want to see a product like a new treatment for disease."
But culture among companies and government-funded labs can vary. Joint efforts mean altering workflows. "It's hard to change behavior," Livermore's Streitz said.
But challenges and high-risk can yield potentially big rewards.
Lab work includes brain-focused research to treat soldiers and other patients for illnesses and injuries such as traumatic brain injury.
Development of a neural device and bionic eye, or retinal prosthesis, largely have been government funded. The retinal implant received more than $75 million over 10 years. The project was conducted under a Cooperative Research and Development Agreement with private sector company Second Sight in Sylmar, California, and included researchers from several national laboratories.
Several neural prosthesis projects have received some $8.1 million in federal funding.
Also housed at Livermore is the National Ignition Facility or NIF—the world's largest laser. It was built for $3.5 billion, and costs around $330 million annually to operate, including related programs.
The facility has many roles, ranging from national security to advancing energy security.
NIF scientists support nuclear weapons maintenance without underground testing—which has been abandoned. Researchers can instead duplicate the phenomena that occurs inside a nuclear device to manage weapons stockpiles.
Experiments at NIF also are laying the groundwork to generate clean energy. The idea is to use lasers to ignite fusion fuel.
If all that doesn't grab you, NIF was used as the set for the "warp core" scene in the 2013 film, "Star Trek Into Darkness."
"The government can pursue grand challenges that are difficult for private companies to do," said Jeff Wisoff, NIF's principal associate director.
—By CNBC's Heesun Wee. Additional reporting by CNBC's Brad Quick.
Correction: This story has been updated to reflect that Frederick Streitz as director of the lab's High Performance Computing Innovation Center.