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We often hear that Machine Learning models learn patterns in data. But what does that actually look like in Geometry? If you dropped a little elastic mesh into a cloud of points and let it learn, how would it fold itself to match the shape of the data? In...

76,194 views • 4 months ago •via X (Twitter)

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The Machine That Learns The Law Behind The Data A very very interesting US Patent US10963540B2 - Physics Informed Learning Machine describes a learning system that does not begin with data alone. It begins with a physical model, usually written as a differential equation (or PDE) dx/dt = f(x,t) A normal Machine Learning model sees scattered data and tries to fit it. A physics-informed learning machine starts with a law. Then it treats the data as evidence that updates what the model believes about the physical system. For this application, I use the patent idea on NASA C-MAPSS Turbofan engine data. The machine watches multivariate telemetry from a degrading engine and infers a hidden health state that is not measured directly. From that posterior belief, it estimates the engine’s remaining useful life. In the main 3D scene, the engine lifetime is turned into a tunnel. The spiral ribbons are real sensor channels evolving over cycle-time. The glowing core is the inferred health state. The surrounding cloud is uncertainty. The orange wall ahead is the predicted failure horizon. So the big picture is: sensor evidence comes in, posterior belief tightens, and the machine moves from uncertainty toward a concrete failure prediction. The inset posteriors make that explicit. The health posterior shows where the model believes the hidden engine condition sits at the current moment, and how sharply it believes it. The RUL posterior shows the same idea for remaining life... early on it is broad, later it shifts left and narrows as the machine becomes more certain about how close failure is. This idea is not limited to engines. The same idea can apply to data centers, CPUs, GPUs, cooling systems, power grids, robotics, batteries, and any machine that produces telemetry while obeying physical constraints. In an age where machine learning runs on massive hardware infrastructure, this kind of model matters: it can turn noisy sensor streams into early warnings before expensive systems fail.

Mathelirium

17,758 views • 2 months ago

New PNAS paper. Historical GDP per capita data is scarce, but data on the places of birth, death, and occupations of famous individuals is abundant. In this paper we estimate the historical GDP per capita of hundreds of regions in Europe and North America using a machine learning model that leveraged data on about 500k famous biographies. Our estimates more-or-less quadruple the availability of historical GDP per capita estimates for the last 700 years. So why use biographies to augment historical GDP per capita data? Biographical data contains information about people who might have contributed directly to economic growth, like James Watt, or that were attracted to wealthy places looking for patrons, like Michelangelo. So we--mainly Philipp (Philipp Koch)--used this data to construct hundreds of features describing each European region. Then, we trained a machine learning model to find the features that explained most of the variance in a cross-validation test, where we split regions multiple times into a training set and a test set. On average, the model explained about 90% of the variance in GDP per capita of the regions it had not seen during training. But we wanted to go further, and Philipp really went to town by looking at different ways to validate our estimates. We found our estimates correlate positively with historical measures of wellbeing, church building activity, urbanization, and body height. We also used these measures to reproduce the basic Atlantic trade result of Acemoglu, Johnson, and Robison and to explore the economic consequences of the famous Lisbon earthquake of 1755. But what I personally loved most about this project, other than working with Philipp Koch and V, is that it shows that we can use machine learning methods not only to explore the future, but the past. There is a bright and growing future in the use of machine learning for economic history. Hope you enjoy the paper and the data. You can find links to the paper and a data exploration tool in the first comment.

César A. Hidalgo

54,332 views • 1 year ago