JuliaCon 2026

Structured light in interaction with matter has been of interest, particularly as it relates to the production of high intensity gamma beams. In our package, ElectronDynamicsModels.jl, we developed a way to efficiently compute the radiated field resulting from the scattering of a Laguerre-Gauss laser beam off a thin sheet of electrons. The electrons are represented as relativistic classical particles whose motion is integrated using DifferentialEquations.jl. ModellingToolkit.jl was used to formulate the model, allowing us to take advantage of its compiler to generate efficient Julia code. Moreover, this also enables an easy scaling to parallel ensemble simulations on the CPU and GPU. Besides performance, this approach is also useful for enabling higher precision computations, which naturally leverage Julia's multiple dispatch. Once the trajectories are known, the far electromagnetic field can be computed over a grid of pixels from the Lienardt-Wiechert potentials, and finally we compute their Fourier transform.

In this talk we will present how DyadModelOptimizer is solving free final time problems using ModelingToolkit, BoundaryValueDiffEq and OptimizationMadNLP, showing the full julia stack that powers the Dyad analyses. Specifically we examine the solution in the context of minimum lap time optimization for a race car. The solution assumes a continuous lap optimizing throttle and braking under dynamical constraints.  We formulate the problem as a nonlinear optimal control problem with free terminal time, where the objective is to minimize total lap time subject to coupled vehicle dynamics, tire force limits, and path constraints along a prescribed track centerline. The vehicle model captures longitudinal and lateral dynamics, load transfer effects, and tire saturation through nonlinear algebraic relationships, resulting in a differential-algebraic system expressed symbolically. The talk walks through the entire process end to end: building the symbolic model, converting it into a boundary value formulation, choosing a discretization strategy, assembling the nonlinear program, and configuring the solver. We will also share practical lessons on mesh refinement, scaling for numerical stability, and what solve times and convergence actually look like in practice.

Real-time adaptive experimental design for ODE models is hard: each step requires costly posterior inference and optimization. We train a neural network policy offline to amortize this cost. The Julia SciML stack makes this practical: Enzyme.jl differentiates through ODEs, Lux.jl defines the policy network, and Reactant.jl compiles everything to a single GPU program. On a bioreactor benchmark, the learned adaptive policy beats Bayesian D-optimal static designs with a 99.5% win rate.

The Dyad platform allows engineers to leverage the power of Julia and SciML via a graphical system modeling environment. The models created by engineers are translated into Julia and harness Julia's just-in-time compilation along with ModelingToolkit's symbolic manipulation capabilities to provide world class simulation performance. But what happens when you want to integrate these models into engineering workflows or wish to leverage the symbolic representations in different ways? In this talk, we'll describe Dyad analyses and how they provide a gateway to the expansive Julia ecosystem.