The U.S. is still out in front of global rivals when it comes to innovation, but American universities –- where new ideas often percolate –- have reason to look over their shoulder.

That’s especially true for technologies like 5G phone networks and artificial intelligence. They’re exactly the fields where President Donald Trump recently insisted the U.S. has to lead — and also the ones where Asia, especially China, has caught up.

Universities from China, Korea and Taiwan get more patents than their U.S. peers in wireless communications, according to research firm GreyB Services. In AI, 17 of the top 20 universities and public research organizations are in China, with the Chinese Academy of Sciences topping the list, says the World Intellectual Property Organization in Geneva. Overall, American universities still dominate the patent rankings, led by the University of California and Massachusetts Institute of Technology.

There’s a special place for universities in the ecosystem of research.

Corporate labs tend to focus on what they’re fairly sure will be profitable, while their government equivalents put national security first. Universities groom future scientist and can be incubators for pie-in-the-sky ideas –- some of which turn out to be game-changers. The list ranges from Google’s search engine to DNA technology that’s behind a whole industry of gene-manipulating treatments. Plus the Honeycrisp apple.

Government grants to universities have been stagnant for more than a decade, meaning they’ve declined in real terms and as a share of the economy.

“If you look at the federal dollars, they’ve not really changed substantially,’’ says Stephen Susalka, head of AUTM, a technology transfer association whose members include 800 universities. “Other countries are catching up. We can’t sit on our laurels.’’

Federal funding of $40 billion for university research in fiscal 2017 was slightly below its peak six years earlier. The colleges spend about $75 billion a year altogether, with the balance largely coming from their own funds. The government’s share has slipped below 60 percent, from almost 70 percent in 2004.

Trump has proclaimed AI and 5G to be high priorities, but hasn’t pitched Congress for more money. In fact, last year the administration called for deep cuts in research funding, including an 11 percent hit to the National Science Foundation.

Congress balked and instead passed the biggest increase for a decade, bringing the total to more than $176 billion. How much will go to universities remains unclear, because the grant process was interrupted by a 35-day government shutdown.

More than half of federal cash for university research comes from the Department of Health and Human Services. That’s reflected in the types of patents U.S. universities are getting. Almost three quarters are in the life sciences, compared with less than half at Asian universities, according to intellectual property-management software firm Anaqua.

‘Should Be More’

Grants for IT research tend to originate at the Pentagon and the NSF, which each contribute about 13 percent of university funding.

“That’s not nothing,’’ says Doug Brake at the Information Technology & Innovation Foundation in Washington. “But I’d argue there should be more,’’ he says. “It pales in comparison to the type of support the Chinese engage in.’’

Comparisons are tricky, but by some measures China’s spending on research and development now rivals America’s.

The Chinese government also is investing in nearly 100 U.S. universities, which have Confucius Institutes to promote Chinese language and culture. None of those schools receive direct U.S. federal funding, according to the Government Accountability Office .

Another way to look at innovation in the world’s two biggest economies, and how they commercialize it, is to study payments made for the use of intellectual property – like patents, trademarks or copyrights. Here again, the U.S. still holds a lead but China is advancing.

The American way of bringing universities into this process has been widely emulated. A 1980 law allows them to keep patents that stem from government-funded research. Universities received more than $3 billion in gross licensing income in 2017, according to AUTM. They filed more than 15,000 patent applications, and helped create 1,080 start-ups.

Walter Copan, head of the National Institute of Standards and Technology, says the system is being updated so that research can be delivered more efficiently into the hands of business.

The government’s job “is to invest in these high-risk exploratory areas,’’ he says. “This is of critical importance to U.S. competitiveness.’’

‘Great to See’

That’s pretty much what Trump concluded about AI in his executive order last month. China isn’t identified by name in the 2,700-word document. But the references to maintaining America’s “economic and national security,’’ and protecting its tech from “attempted acquisition by strategic competitors,’’ point clearly in that direction.

Money doesn’t get much of a mention, though. At the University of California in Berkeley, there’s significantly more high-quality work going on than there is cash available, says Randy Katz, the vice chancellor for research. Only about one in five proposals deemed to have merit ends up getting funded.

That’s why Trump’s AI order needs some practical follow-up, says Katz. “It’s great to see it’s a national priority,” he says. “It’s up to Congress to see how much money is going to be spent.’’