Physics on Dan MacKinlay
https://danmackinlay.name/tags/physics.html
Recent content in Physics on Dan MacKinlayHugo -- gohugo.ioen-usTue, 13 Apr 2021 16:24:05 +0800Machine learning for partial differential equations
https://danmackinlay.name/notebook/ml_pde.html
Tue, 13 Apr 2021 16:24:05 +0800https://danmackinlay.name/notebook/ml_pde.htmlLearning a PDE Deterministic PINN Stochastic PINN Weak formulation Learning a PDE forward operator Fourier neural operator DeepONet Advection-diffusion PDEs in particular Boundary conditions Inverse problems Differentiable solvers DeepXDE ADCME TenFEM JuliaFEM Trixi FEniCS taichi References Using statistical or machine learning approaches to solve PDEs, and maybe even to perform inference through them. There are various approaches here, which I will document on an ad hoc basis as I need them.Hydrology models
https://danmackinlay.name/notebook/hydrology.html
Tue, 13 Apr 2021 14:36:12 +0800https://danmackinlay.name/notebook/hydrology.htmlTools Simulation Geostats Framework Datasets References Refugees from Brazil’s Grande Seca drought of 1878
TBD: Ground water hydrology, surface water hydrology, coastal water hydrology… UCSB Climate hazards data.
Tools Simulation AFAICT the go-to applied reference here is Anderson, Woessner, and Hunt (2015).
MODFLOW
MODFLOW is the USGS’s modular hydrologic model. MODFLOW is considered an international standard for simulating and predicting groundwater conditions and groundwater/surface-water interactions.Machine learning for physical sciences
https://danmackinlay.name/notebook/ml_physics.html
Fri, 09 Apr 2021 11:48:30 +0800https://danmackinlay.name/notebook/ml_physics.htmlML for PDEs Causality, identifiability, and observational data Likelihood free inference Emulation approaches The other direction: What does physics say about learning? But statistics is ML Applications References Consider a spherical flame
In physics, typically, we are concerned with identifying True Parameters for Universal Laws, applicable without prejudice across all the cosmos. We are hunting something like the Platonic ideals that our experiments are poor shadows of.Stochastic processes which represent measures over the reals
https://danmackinlay.name/notebook/measure_priors.html
Mon, 08 Mar 2021 16:44:16 +1100https://danmackinlay.name/notebook/measure_priors.htmlSubordinators Other measure priors References Often I need to have a nonparametric representation for a measure over some non-finite index set. We might want to represent a probability, or mass, or a rate. I might want this representation to be something flexible and low-assumption, like a Gaussian process. If I want a nonparametric representation of functions this is not hard; I can simply use a Gaussian process.Convolutional subordinator processes
https://danmackinlay.name/notebook/subordinator_convolution.html
Mon, 08 Mar 2021 15:29:19 +1100https://danmackinlay.name/notebook/subordinator_convolution.htmlReferences Stochastic processes by convolution of noise with smoothing kernels, where the driving noise is a Lévy subordinator.
Why would we want this? One reason is that this gives us a way to create nonparametric distributions over measures.
References Barndorff-Nielsen, O. E., and J. Schmiegel. 2004. “Lévy-Based Spatial-Temporal Modelling, with Applications to Turbulence.” Russian Mathematical Surveys 59 (1): 65. https://doi.org/10.1070/RM2004v059n01ABEH000701. Çinlar, E. 1979. “On Increasing Continuous Processes.Convolutional Gaussian processes
https://danmackinlay.name/notebook/gp_convolution.html
Mon, 01 Mar 2021 17:08:51 +1100https://danmackinlay.name/notebook/gp_convolution.htmlConvolutions with respect to a non-stationary driving noise Varying convolutions with respect to a stationary white noise References Gaussian processes by convolution of noise with smoothing kernels, which is a kind of dual to defining them through covariances.
This is especially interesting because it can be made computationally convenient (we can enforce locality) and non-stationarity.
Convolutions with respect to a non-stationary driving noise H. K.Convolutional stochastic processes
https://danmackinlay.name/notebook/stochastic_convolution.html
Mon, 01 Mar 2021 16:13:24 +1100https://danmackinlay.name/notebook/stochastic_convolution.htmlReferences Stochastic processes generated by convolution of white noise with smoothing kernels, which is not unlike kernel density estimation where the “data” is random.
For now, I am mostly interested in certain special cases Gaussian process convolutionss and subordinator convolutions.
patrick-kidger/Deep-Signature-Transforms: Code for "Deep Signature Transforms" patrick-kidger/signatory: Differentiable computations of the signature and logsignature transforms, on both CPU and GPU. References Bolin, David.Statistical mechanics of statistics
https://danmackinlay.name/notebook/statistical_mechanics_of_statistics.html
Wed, 06 Jan 2021 12:46:59 +1100https://danmackinlay.name/notebook/statistical_mechanics_of_statistics.htmlPhase transitions in statistical inference Replicator equations and evolutionary processes References Boaz Barak has a miniature dictionary for statisticians:
I’ve always been curious about the statistical physics approach to problems from computer science. The physics-inspired algorithm survey propagation is the current champion for random 3SAT instances, statistical-physics phase transitions have been suggested as explaining computational difficulty, and statistical physics has even been invoked to explain why deep learning algorithms seem to often converge to useful local minima.Multi-output Gaussian process regression
https://danmackinlay.name/notebook/gp_regression_functional.html
Mon, 07 Dec 2020 20:43:06 +1100https://danmackinlay.name/notebook/gp_regression_functional.htmlReferences In which I discov Learning operators via GPs.
References Brault, Romain, Florence d’Alché-Buc, and Markus Heinonen. 2016. “Random Fourier Features for Operator-Valued Kernels.” In Proceedings of The 8th Asian Conference on Machine Learning, 110–25. http://arxiv.org/abs/1605.02536. Brault, Romain, Néhémy Lim, and Florence d’Alché-Buc. n.d. “Scaling up Vector Autoregressive Models With Operator-Valued Random Fourier Features.” Accessed August 31, 2016. https://aaltd16.irisa.fr/files/2016/08/AALTD16_paper_11.pdf. Brouard, Céline, Marie Szafranski, and Florence D’Alché-Buc.Emulators and surrogate models
https://danmackinlay.name/notebook/ml_emulation.html
Wed, 26 Aug 2020 15:12:14 +1000https://danmackinlay.name/notebook/ml_emulation.htmlReferences Emulation, a.k.a. surrogate modelling. In this context, it means reducing complicated physics-driven simulations to simpler/or faster ones using ML techniques. Especially popular in the ML for physics pipeline. I have mostly done this in the context of surrogate optimisation for experiments.
A recent, hyped paper that exemplifies this approach is Kasim et al. (2020), which (somewhat implicitly) uses arguments from Gaussian process regression to produce quasi-Bayesian emulations of notoriously slow simulations.Multi fidelity models
https://danmackinlay.name/notebook/multi_fidelity.html
Mon, 24 Aug 2020 09:58:14 +1000https://danmackinlay.name/notebook/multi_fidelity.htmlReferences TBD
References Cutajar, Kurt, Mark Pullin, Andreas Damianou, Neil Lawrence, and Javier González. 2019. “Deep Gaussian Processes for Multi-Fidelity Modeling.” March 18, 2019. http://arxiv.org/abs/1903.07320. Kennedy, M. C., and A. O’Hagan. 2000. “Predicting the Output from a Complex Computer Code When Fast Approximations Are Available.” Biometrika 87 (1): 1–13. https://doi.org/10.1093/biomet/87.1.1. Kennedy, Marc C., and Anthony O’Hagan. 2001. “Bayesian Calibration of Computer Models.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (3): 425–64.Bushfire models
https://danmackinlay.name/notebook/bushfires.html
Wed, 19 Aug 2020 11:34:20 +1000https://danmackinlay.name/notebook/bushfires.htmlReferences american forest fire 1904
Press: Silicon valley wildfire spotting.
References Hilton, J. E., A. L. Sullivan, W. Swedosh, J. Sharples, and C. Thomas. 2018. “Incorporating Convective Feedback in Wildfire Simulations Using Pyrogenic Potential.” Environmental Modelling & Software 107 (September): 12–24. https://doi.org/10.1016/j.envsoft.2018.05.009. Mandel, Jan, Jonathan D. Beezley, Janice L. Coen, and Minjeong Kim. 2009. “Data Assimilation for Wildland Fires.” IEEE Control Systems Magazine 29 (3): 47–65.Quantum computing
https://danmackinlay.name/notebook/quantum_computing.html
Sat, 23 May 2020 08:13:15 +1000https://danmackinlay.name/notebook/quantum_computing.htmlTopical Courses Emulations, languages References Nothing to see here yet apart from some links I myself don’t have time to inspect.
Topical Scott Aaronsons’s Quantum supremacy FAQ, What Google’s Quantum Supremacy Claim Means for Quantum Computing Preskill on quantum supremacy Stephen Jordan’s Quantum Algorithm Zoo Courses Scott Aaronsons’s his lecture notes on quantum computing now available as preprint textbook
His introduction also has some useful leads:Learning with conservation laws, invariances and symmetries
https://danmackinlay.name/notebook/learning_with_conservation_laws.html
Fri, 01 May 2020 09:53:27 +1000https://danmackinlay.name/notebook/learning_with_conservation_laws.htmlReferences Failure of conservation of mass at system boundaries is a common problem in models with nonparametric likelihood
Learning in complicated systems where we know that there is a conservation law in effect. Or, more advanced, learning a conservation law that we did not know was in effect. As seen in especially ML for physics. This is not AFAIK a particular challenge in traditional parametric statistics where we can impose conservation laws on a problem through the likelihood, but nonparametrics models, or models with overparameterisation such as neural nets this can get fiddly.Hamiltonian and Langevin Monte Carlo
https://danmackinlay.name/notebook/hamiltonian_monte_carlo.html
Thu, 12 Jul 2018 21:07:16 +1000https://danmackinlay.name/notebook/hamiltonian_monte_carlo.htmlLangevin Monte Carlo To file References Hamiltonians, energy conservation in sampling. Handy. Summary would be nice.
Michael Betancourt’s heuristic explanation of Hamiltonian Monte Carlo: sets of high mass, no good - we need the “typical set”, a set whose product of differential volume and density is high. Motivates Markov Chain Monte Carlo on this basis, a way of exploring typical set given points already in it, or getting closer to the typical set if starting without.Quantum information in physics
https://danmackinlay.name/notebook/quantum_information.html
Thu, 14 Dec 2017 16:26:26 +1100https://danmackinlay.name/notebook/quantum_information.htmlI would like to understand this more deeply, through following up the references in this piece:
Scott Aaronson, Is “information is physical” contentful?
“Information is physical.”
This slogan seems to have originated around 1991 with Rolf Landauer. […] There are many things it’s taken to mean, in my experience, that don’t make a lot of sense when you think about them-- or else they’re vacuously true, or purely a matter of perspective, or not faithful readings of the slogan’s words.Lagrangian mechanics
https://danmackinlay.name/notebook/lagrangian_mechanics.html
Sun, 18 Jun 2017 08:01:47 +0800https://danmackinlay.name/notebook/lagrangian_mechanics.htmlApplied variational calculus with some physics.
I don’t really do physics these days, but physicists write the best introductions to variational calculus, which I do do.
“What is the quickest path through these mountains?” “Where do I put mountains such that my map produces the right quickest path?”
Optimal control, Pontryagin’s maximum principle. Variational calculus, minimising functionals. Deriving high dimensional functions as solutions of scalar optimisation using conservation principles as seen in functional data analysis and variational inference.Special functions
https://danmackinlay.name/notebook/special_functions.html
Wed, 21 Dec 2016 13:55:33 +0100https://danmackinlay.name/notebook/special_functions.htmlErf Gamma function Bessel functions t-density A wunderkammer of useful curves.
Otto Lueger, 1904, Lexikon der gesamten Technik (dictionary of technology).
Chaitanya Rao, Some special functions and their applications: Bessel and related functions (Hankel, Airy), Hermite, Laguerre, Chebychev, Legendre polynomials, various fun integrals such as Fresnel integrals, Erf and so on, as made popular by all of functional analysis and its application in function approximation.Material basis of the economy
https://danmackinlay.name/notebook/material_basis_of_the_economy.html
Mon, 01 Aug 2016 16:02:18 +0100https://danmackinlay.name/notebook/material_basis_of_the_economy.htmlTo Read Energetics References UCL and Kiln visualising every ship on earth in 2012
See shipmap for more of that.
See also:
innovation configuration space of the economy intellectual property To mention: Exergy, emergy, various footprint measures. The mysteries of trade: why do countries who export cars also import cars?
What is growth? Do we have to burn petroleum to have it? Is it bad if we don’t have it?Thermodynamics
https://danmackinlay.name/notebook/thermodynamics_of_computation.html
Mon, 18 Jan 2016 09:38:34 +1100https://danmackinlay.name/notebook/thermodynamics_of_computation.htmlMorsels from physics-write-large.
Explain this relative to algorithmic statistics again?
The end of the thermodynamics of computation?
Baez on The Mathematical Origin of Irreversibility
Could it be that thermal phenomena, forgetful information processing and adaptive evolution are governed by the same stochastic mechanism?
The answer is — yes! The key to this rather profound connection resides in a universal property of Markov processes discovered recently in the context of non-equilibrium statistical mechanics, and known as the ‘fluctuation theorem’.Earthquakes
https://danmackinlay.name/notebook/earthquakes.html
Tue, 14 Jul 2015 14:44:35 +0200https://danmackinlay.name/notebook/earthquakes.htmlKircher’s model of the seismic systems of the earth
A passing interest of mine, caught from Didier Sornette when we was my supervisor.
I’m mostly interested in the self-exciting process model of Ogata and Ozaki et al, but I’ll also accept notes on human tragedy and normal accidents.
Kathryn Schulz at the New Yorker The Really Big One
To see the full scale of the devastation when that tsunami recedes, you would need to be in the international space station.