This paper presents a method for uncovering hidden analytic relationships among the fundamental parameters of the Standard Model (SM), a foundational theory in physics that describes the fundamental particles and their interactions, using symbolic regression and genetic programming. Using this approach, we identify the simplest analytic relationships connecting pairs of these constants and report several notable expressions obtained with relative precision better than 1%. These results may serve as valuable inputs for model builders and artificial intelligence methods aimed at uncovering hidden patterns among the SM constants, or potentially used as building blocks for a deeper underlying law that connects all parameters of the SM through a small set of fundamental constants.

Humans can reason about intuitive physics in fully or partially observed environments even after being exposed to a very limited set of observations.

We present a new method for enhancing symbolic regression for differential equations via dimensional analysis, specifically Ipsen's and Buckingham pi methods. Since symbolic regression often suffers from high computational costs and overfitting, non-dimensionalizing datasets reduces the number of input variables, simplifies the search space, and ensures that derived equations are physically meaningful. As our main contribution, we integrate Ipsen's method of dimensional analysis with Universal Physics-Informed Neural Networks. We also combine dimensional analysis with the AI Feynman symbolic regression algorithm to show that dimensional analysis significantly improves the accuracy of the recovered equation. The results demonstrate that transforming data into a dimensionless form significantly decreases computation time and improves accuracy of the recovered hidden term. For algebraic equations, using the Buckingham pi theorem reduced complexity, allowing the AI Feynman model to converge faster with fewer data points and lower error rates. For differential equations, Ipsen's method was combined with Universal Physics-Informed Neural Networks (UPINNs) to identify hidden terms more effectively. These findings suggest that integrating dimensional analysis with symbolic regression can significantly lower computational costs, enhance model interpretability, and increase accuracy, providing a robust framework for automated discovery of governing equations in complex systems when data is limited.

Interleaved practice enhances the memory and problem-solving ability of students in undergraduate courses. We introduce a personalized learning tool built on a Large Language Model (LLM) that can provide immediate and personalized attention to students as they complete homework containing problems interleaved from undergraduate physics courses. Our tool leverages the dimensional analysis method, enhancing students' qualitative thinking and problem-solving skills for complex phenomena. Our approach combines LLMs for symbolic regression with dimensional analysis via prompt engineering and offers students a unique perspective to comprehend relationships between physics variables. This fosters a broader and more versatile understanding of physics and mathematical principles and complements a conventional undergraduate physics education that relies on interpreting and applying established equations within specific contexts. We test our personalized learning tool on the equations from Feynman's lectures on physics. Our tool can correctly identify relationships between physics variables for most equations, underscoring its value as a complementary personalized learning tool for undergraduate physics students.

When developing empirical equations, domain experts require these to be accurate and adhere to physical laws. Often, constants with unknown units need to be discovered alongside the equations. Traditional unit-aware genetic programming (GP) approaches cannot be used when unknown constants with undetermined units are included. This paper presents a method for dimensional analysis that propagates unknown units as ''jokers'' and returns the magnitude of unit violations. We propose three methods, namely evolutive culling, a repair mechanism, and a multi-objective approach, to integrate the dimensional analysis in the GP algorithm. Experiments on datasets with ground truth demonstrate comparable performance of evolutive culling and the multi-objective approach to a baseline without dimensional analysis. Extensive analysis of the results on datasets without ground truth reveals that the unit-aware algorithms make only low sacrifices in accuracy, while producing unit-adherent solutions. Overall, we presented a promising novel approach for developing unit-adherent empirical equations.

We present a framework for constraining the automatic sequential generation of equations to obey the rules of dimensional analysis by construction. Combining this approach with reinforcement learning, we built $\Phi$-SO, a Physical Symbolic Optimization method for recovering analytical functions from physical data leveraging units constraints. Our symbolic regression algorithm achieves state-of-the-art results in contexts in which variables and constants have known physical units, outperforming all other methods on SRBench's Feynman benchmark in the presence of noise (exceeding 0.1%) and showing resilience even in the presence of significant (10%) levels of noise.

Yes if the context, the list of variables defining the motion control problem, is dimensionally similar. Here we show that by modifying the problem formulation using dimensionless variables, we can re-use the optimal control law generated numerically for a specific system to a sub-space of dimensionally similar systems. This is demonstrated, with numerically generated optimal controllers, for the classic motion control problem of swinging-up a torque-limited inverted pendulum. We also discuss the concept of regime, a region in the space of context variables, that can help relax the condition on dimensional similarity. Futhermore, we discuss how applying dimensionnal scaling of the input and output of a context-specific policy is equivalent to substituing the new systems parameters in an analytical equation for dimentionnaly similar systems. It remains to be seen if this approach can also help generalizing policies for more complex high-dimensional problems.

Trading is one of the easiest activities around: few seconds and you are in position, few seconds and you are out of your position. Making it profitable is a totally different discourse. Libraries are plenty of technical and fundamental analysis books and the internet is plenty of websites that offer amazing returns. All of them (except some you can count on one hand's fingers) do the same one dimensional analysis, based on the tape, the fluctuating price of the chosen instrument. The variety of tools available is confusing, but basically they all work on moving averages and momentum, sometimes volatility.

When I was in high school, I had a superb chemistry teacher, something I, unfortunately, failed to appreciate until long after I went to college. For the first year of AP chemistry, we spent a huge amount of time working on what was at the time called unit analysis, though from a modeling perspective this is now known as dimensional analysis. It is, sadly, something of a lost art, and it's something that trips up people far more often than it should. Dimensional analysis, in its purest form, can be summarized as the statement "You can't compare apples to oranges." Put another way, if you add three apples to two oranges, you do not have five apples.