Ethics statement
IMPORTANT: all algorithms, sampled data, and implementation is done in the absence of demographic bias (all “random” synthetic adjustments to data was performed using a normal distribution centered at 0 with std = 2). Research bias may exist but is not significant when considering real-world use cases.
This algorithm can be considered fair and unbiased. No generative AI was used in ideation, development, and deployment.
Inspiration
In a world that is rapidly changing due to computers, algorithms, and data, we want to find ways to make these computational tools faster and more efficient.
Inspired by a typical rate-limiting factor in these algorithms, numerical integration, we wanted to find a way to make this process faster. Utilizing a type of calculation called “a priori” computing, we found a way to run simulations of stellar transfer and orbital mechanics faster than traditional methods. Both of these problems are common for astronomers who want to use simulations rather than empirical observations.
Our algorithm, Stellar AXIS, makes both of these calculations much more efficient than with SOTA techniques. Additionally, accuracy has remained similar and even higher than these classic methods.
What it does
The core process of Stellar AXIS uses a modified loss (see Theorem 2 from the Technical Whitepaper) to match the derivative of a neural network to an integrand function. When the network trains, it approximates the antiderivative function. This functional representation can then be used simply by plugging in the desired bounds and taking differences (the fundamental theorem of calculus).
Other advancements (adaptive colocation, expressiveness/initialization, and the genetic algorithm/crossover) make Stellar AXIS even more effective.
We derive a sample integrand function for radiative transfer, and test it by rapidly changing bounds (optical depths in ) to calculate luminous intensity. When compared to a SOTA method (Gaussian quadrature), Stellar AXIS performs faster and to the same degree of accuracy.
For orbital transfer, the time-of-flight (TOF) was computed using another sample integrand function and was integrated over two true anomalies. This simulation also performed better than SOTA methods.
If you would like a rigorous assessment and overview of our mathematics, please refer to the Technical Whitepaper linked below!
How we built it
We implemented all code in Python, using Google Colab, taking advantage of TPUs for fast tensor processing. When dealing with large networks and intractable gradients, high-ram A100s were needed.
Challenges we ran into
We ran into a few challenges: the math we were dealing with was excessively complex, we needed a lot of computational resources to train our models, and writing the simulation code and visualizing it in an easy way was difficult.
We got around this issues by purchasing more powerful GPUs and server spaces in Colab, and studying the math for hours until we developed proofs.
Accomplishments that we're proud of
This methodology is completely novel, and has the potential to speed up algorithms in many different places, not just in the two problems we discuss here. Additionally, we backed up our empirical results by proving our claims, and then got these theorems validated by a real scientist.
Additionally, we think our graphical presentation is aesthetic while also being informative.
What we learned
We learned a lot about computational mathematics, orbital transitions, and radiative transfer, while also understanding how theoretical considerations and algorithms can be brought into real-world use.
What's next for Stellar AXIS
We want to expand to other use cases!
Credits
Grace Pan — Ideation, mathematical proofs, computational implementation
KT Mozzo — Ideation, data / simulation visualization, computational implementation
Hasita Alluri — Ideation, mathematical presentation, simulation visualization
Nikhil Vemuri — Ideation, graphical presentation, validation (reached out for mathematical validation by experts)
Our Technical Whitepaper was validated by Dr. Daniel Egger of Duke University for completeness and correctness. We would like to thank him for his assistance and time.
Built With
- algorithms
- calculus
- differential-equations
- machine-learning
- python
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