The last set of cross-validation results are based on training of held-out data for intervals outside of 0.6-0.8 (i.e. training on t<0.6 and t>0.8 of the data, which extends from t=0.0 to t=1.0 normalized). This post considers training on intervals outside of 0.3-0.6 — a narrower training interval and correspondingly wider test interval.
Each fitted model result shows the cross-validation results based on training of held-out data — i.e. training on only the intervals outside of 0.6-0.8 (i.e. training on t<0.6 and t>0.8 of the data, which extends from t=0.0 to t=1.0 normalized). The best results are for time-series that have 100 years or more worth of monthly data, so the held-out data is typically 20 years. There is no selection bias trickery here, as this is a collection of independent sites and nothing in the MLR fitting process is specific to an individual time-series. In the following, the collection of results starts with the Stockholm site in Sweden, keeping in mind that the dashed line in the charts indicates the test or validation interval.
A paper from last week with high press visibility that makes claims to climate1 applicability is titled: Topology shapes dynamics of higher-order networks
The higher-order Topological Kuramoto dynamics, defined in Eq. (1), entails one linear transformation of the signal induced by a boundary operator, a non-linear transformation due to the application of the sine function, concatenated by another linear transformation induced by another boundary operator. These dynamical transformations are also at the basis of simplicial neural architectures, especially when weighted boundary matrices are adopted.
This may be a significant unifying model as it could resolve the mystery of why neural nets can fit fluid dynamic behaviors effectively without deeper understanding. In concise terms, a weighted sine function acts as a nonlinear mixing term in a NN and serves as the non-linear transformation in the Kuramoto model2.
Continue readingRemove m-u-l-e-c-a-d. Mul tid ecad al
These each have a substantial back and forward cross-validation interval.
Continue readingTrying out a presentation
The Gist site on GitHub allows you to comment on posts very easily. For example, images of charts can be pasted in the discussion area. Also snippets of code can be added and updated, which is useful for neural net evaluation. The following is a link to an initial Gist area for evaluating LTE models.
It’s been over 10 years since a thread on simplifying climate models was posted on the Azimuth Project forum => https://forum.azimuthproject.org/discussion/981/the-fruit-fly-of-climate-models
A highly esteemed climate scientist, Isaac Held, even participated and voiced his opinion on how feasible that would be. Eventually the forum decided to concentrate on the topic of modeling El Nino cycles, starting out with a burst of enthusiasm. The independent track I took on the forum was relatively idiosyncratic, yet I thought it held promise and eventually published the model in the monograph Mathematical Geoenergy (AGU/Wiley) in late 2018. The forum is nearly dead now, but there is recent thread on “Physicists predict Earth will become a chaotic world”. Have we learned nothing after 10 years?
My model assumes that El Nino/La Nina cycles are not chaotic or random, which is still probably considered blasphemous. In contrast to what’s in the monograph, the model has simplified, and a feasible solution can be mapped to data within minutes. The basic idea remains the same, explained in 3 parts.
The fitting process is to let all the parameters to vary slightly and so I use the equivalent of a gradient descent algorithm to guide the solution. The impulse month is seeded along with starting guesses for the two slowest wavenumbers. Another MLR algorithm is embedded to estimate the amplitude and phases required.
The multi-processing software is at https://github.com/pukpr/GeoEnergyMath/wiki
Recently it has taken mere minutes to arrive at a viable model fit to the ENSO data (the ENS ONI monthly data (1850 – Jul 2022)), starting with the initially calibrated dLOD factors. Each of the tidal factors is modified slightly but the correlation coefficient is still at 0.99 of the starting dLOD.
Even with that, the only way to make a convincing argument is to apply cross-validation during the fitting process. A training interval is used during the fitting and the model is extrapolated as a check once the training error is minimized. Even though the model is structurally sensitive, it does not show wild over-fitting errors. This is explainable as only a handful of degrees of freedom are available.
So this demonstrates that the behavior is stationary and definitely not chaotic, only obscured by the non-linear modulation applied to tidally forced waveform.
Informative article on development of cusped waveforms and Kelvin-Helmholtz instabilities
Amazing number of harmonics
https://www.sciencedirect.com/science/article/pii/B9780128215128000177
The most important mechanism for turbulence production in equatorial parallel shear flows is the inflectional instability, which operates at local maxima of the mean shear profile (Smyth and Carpenter, 2019). In the presence of stable stratification, inflectional instability is damped, but it may yet grow, provided that the minimum value of Ri is less than critical. In this case, the process is termed Kelvin–Helmholtz (KH) instability.
In Chapter 10 of the book we touch on organization of environmental models.
“Furthermore, by applying ontology‐based approaches for organizing models and techniques, we can set the stage for broader collections of such models discoverable by a general community of designers and analysts. Together with standard access protocols for context modeling,
Energy Transition : Applying Probabilities and Physics
these innovations provide the promise of making environmental context models generally available and reusable, significantly assisting the energy analyst.”
Although we didn’t elaborate on this topic, it is an open area for future development, as our 2017 AGU presentation advocates. The complete research report is available as https://doi.org/10.13140/RG.2.1.4956.3604.
What we missed on the first pass was an ontology for citations titled CiTO (Citation Typing Ontology) which enables better classification and keeping track of research lineage. The idea again is to organize and maintain scientific knowledge for engineering and scientific modeling applications. As an example, one can readily see how the Citation Typing Ontology could be applied, with the is_extended_by object property representing much of how science and technology advances — in other words, one finding leading to another.
