Over the past decade, the 19th century science-of-counting was resurrected to provide a combinatorial derivation of conventional Machine Learning that uniquely generalizes statistics to probability theory, allows energy to enter or exit the system, and processes any time-series to return a complete set of scientific (thermodynamic) measurements as deductive reality [1].
Conventional machine learning is effective in static, closed world applications, but does not accommodate changing environments, where energy can enter or exit, or, where energy is stored temporarily for later release. Energy that enters or exits a system should also include emotional energy, as it is the principle and obvious source of human energy that can both affect the dynamics of counting and anticipate a need.
Scientific machine learning is the combinatorial science-of-counting evaluated on time-series that reduces correctly to statistics when there is no energy entering or exiting the system. With a constructivist approach to generalized Machine Learning for time-series, we observe that “Machine” and “Artificial Intelligence” are too prominent in this presentation, because in the science-of-counting computers only do what they have done from their inception: evaluate built-in functions. The conception and derivation of the scientific functions is human intelligence. In the science-of-counting “scientific machine learning” will be simplified to scientific learning.
We see that the human mind (intuition, intellect and emotions) is a gift capable of deducing reality. On the other hand, human invention is absent because what we know follows from deduction, and is free from human caprice.
By examining problems that share the same overall mathematical structure as Scientific Learning, the power grid is seen to be historically founded on the science-of-counting with a key engineering assumption/simplification, the average of the strain vanishes so that strain can be ignored. Strain can be ignored only at statistical equilibrium, when the system is just as likely to go up as to go down. The traditional power grid could ignore strain, because power generation was controlled and predictable. But given renewable energy sources, the next generation of power grid must recognize and manage power grid resistance and stored energy in order to manage supply and demand.
When applied to a “need”, say, electrical power, Scientific Learning becomes a Science of Giving and Receiving at Scale. With both supply and demand time-series, the power grid realizes the Science of Giving and Receiving and inherits the analytical benefits. The science of giving and receiving is used to re-architect the electrical power grid for non-equilibrium operation that can better support variable energy sources (renewables). The power grid of the future is a re-engineering problem that will not be solved by government policy alone.
Supply and Demand Interactions
The functions that define the relationship between energy, momentum and velocity, E=pv, are deduced in the science-of-counting (the dispersion relation) [1]. To manage supply and demand the same analysis is deductively extended to interactions as well. A high-level picture of the interaction science is presented here.
Given a time-series for electrical energy supply (in MWh), \(n_A\), there are natural coordinates (an eigenbasis) in scientific learning that define the Expected Supply and its associated Expected Strain. Similarly, given a time-series for energy demand (in MWh), \(n_B\), the Expected Demand and its associated Expect Strain are defined. The Lagrangian below enforces supply and demand measurements as constraints, \(\cal{L}_A\) and \(\cal{L}_B\), and moreover adds the constraints for interaction measurements, with the Lagrange multipliers \(\lambda_{AB}\) and the \(\sigma_{AB}\) terms below.
\[\begin{align} \cal{L} &= \cal{L}_A + \cal{L}_B - \lambda_{AB}\,<n_A\,n_B> - \,\sigma_{AB}\,<v_A\,v_B>. \end{align}\]If the supply and demand time-series are independent, that is, there is no interaction between the two, then the time-series couplings \(\lambda_{AB}\) and \(\sigma_{AB}\) both vanish, and \(p(n_A n_B) = p(n_A)p(n_B)\). In truth, of course, supply and demand are highly coupled and interact non-trivially. We introduce the interaction function, \(\Lambda\), of the two time-series defined by
\[\begin{align} \Lambda \equiv \frac{p(n_A)p(n_B)}{p(n_A n_B)},\quad p(n_A n_B) = \Lambda (1-\Lambda), \quad \Lambda = \frac{1}{2} \pm \sqrt{\frac{1}{4} - p(n_A n_B)}. \end{align}\]Since energy can enter and exit, the interaction diagram and coupling curve are for inelastic scattering.
Using the following identities,
\[\begin{align} \frac{y}{x} = \frac{p(n_A n_B)}{p(n_A)p(n_B)} = \frac{p(n_A\vert n_B)}{p(n_A)} = \frac{p(n_B\vert n_A)}{p(n_B)}, \end{align}\]the curve is the same but the axis labels \(x\) and \(y\) define a different problem: forward and backward scattering, supply needed for demand, demand needed for supply, respectively. Thus providing several opportunities for deterministic control of the system.
To Give and To Receive
The introduction of money breaks the deductive structure of scientific learning, which we have worked hard to preserve. The moment we introduce currency, models are introduced, in this case, exchange rate models that convert money to displacement energy. Expect every business process to have its own exchange rate, the spend for a set displacement energy. Exchange rate models imply some degree of control with the right spend, from which we manage supply and demand scientifically.
Giving should meet both physical and spiritual needs, including instruction, counsel, comfort and forgiveness. For St. Thomas Aquinas, giving and receiving are not merely economic or social acts. They are moral, spiritual and relational realities that mirror the very life of God.