There is a joke in applied mathematics that we’re like Taco Bell. We all use the same six ingredients, mixing them in different ways.
For myself, I’ve found several techniques I use over and over again. Some of this is a “when you’re a hammer, everything looks like a nail.” But fundamentally there are only a handful of ideas. One professor of mine once said the only groundbreaking result in the past few decades was compressive sensing.
When I was working with NREL back in 2017, they were thinking about coordinating water heater electricity use with a “smart grid.” Each device attached to the smart grid would measure the electricity spot price and would “store” energy to minimize cost. At the time the goal was to reduce peak load on the grid, but the same ingredients to maximize power use from intermittent power sources.
"Deep defense cuts. Since the 1980s, the Pentagon budget has fallen from 6% to 3% of GDP—not far above Europe’s target of 2%. Cutting U.S. defense spending to the levels pledged by European members of NATO would save 1% of GDP, or less than one-fifth of the Social Security and Medicare noninterest shortfall by the 2040s and 2050s."
Read the budget. Learn something. None of the partisan mantras solve the problem. The only solution is to trim ss, trim medicare, and raise taxes across the board.
I concur. As a postdoc for many years adjacent to this work, I was similarly unimpressed.
The best part about PINNs is that since there are so many parameters to tune, you can get several papers out of the same problem. Then these researchers get more publications, hence better job prospects, and go on to promote PINNs even more. Eventually they’ll move on, but not before having sucked the air out of more promising research directions.
I taught numerical linear algebra in grad school and was really frustrated that even the applied math department took so long to build up to solving linear systems and eigen-decompsotions. The ordering of the material in the textbook is great, focusing on algorithms and decompositions.
The first space shuttle prototype (Enterprise) started construction in 1974. The first shuttle launched in 1981. To the best of my knowledge, there were no major upgrades to the design over its career, save avionics. So even though the space shuttle was “serious space development,” it’s been a long time since a new human rated vehicle has been designed.
It would be great if that tool existed, but it doesn’t seem to right now. I can appreciate the instinct to improve packaging, but from an occasional Python developer’s perspective things are getting worse. I published a few packages before the pandemic that had compiled extensions. I tried to do the same at my new job and got so lost in the new tools, I eventually just gave up.
One of Python’s great strengths is the belief there should be one, obvious right way to things. This lack of unity in the packing environment is ruining my zen.
As someone who works in numerical optimization, this is a dirty little secret of our profession. The optimization algorithms in the literature are great at finding local minima, but often are very sensitive to the initialization as to how small the objective is. Good heuristics for initialization are thus critical for finding a good (small objective) minimizer. Sometimes this gets to the point where the local optimization algorithm does a trivial refinement of the heuristic’s solution.
For myself, I’ve found several techniques I use over and over again. Some of this is a “when you’re a hammer, everything looks like a nail.” But fundamentally there are only a handful of ideas. One professor of mine once said the only groundbreaking result in the past few decades was compressive sensing.
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