Manim Slides

Welcome everyone, and thank you for being here today. My name is Jérome Eertmans, and I will present my PhD work on differentiable ray tracing for radio propagation modeling.

Let me start by providing a brief context. In wireless communications, understanding how radio waves propagate through complex environments is essential. Ray tracing is a simulation technique that traces individual ray paths from a transmitter to a receiver.

RT models the key electromagnetic interactions: reflection off surfaces, diffraction around edges, and scattering from rough surfaces.

Radio waves travel through complex environments like cities.

RT simulates individual paths between TX and RX.

Each path can undergo multiple interactions.

This enables site-specific channel modeling.

So why differentiable ray tracing? The key idea is to make the entire RT simulation pipeline differentiable, meaning we can compute gradients of any output with respect to any input.

Differentiable RT motivation bullet.

This represents a paradigm shift: from traditional CPU-based non-differentiable RT to GPU-enabled, optimization-ready differentiable RT.

To differentiable, GPU-enabled ray tracing.

These motivations come with several practical challenges, which are the central theme of my thesis.

Challenge bullet.

My thesis addresses these challenges through three main contributions, which I will now present in chronological order.

Before diving into the contributions, let me give you an overview of my PhD journey. This timeline highlights the key milestones, from my student jobs in 2020 through the start of my PhD in 2021, several conferences and research stays, up to EuCAP 2026 just a few weeks ago.

The timeline of my PhD journey.

I will focus on three main contributions, highlighted here: the smoothing technique, the ML-based path tracing, and the Fermat Path Tracing method.

Here is the roadmap for this presentation. After the context we just covered, I will present each of my three main contributions in chronological order, followed by a conclusion with future directions.

Let me now present the first contribution. It all starts with the path tracing problem: given a TX and RX and a sequence of interactions, we want to find the path that minimizes the total optical length, following Fermat's principle.

The min. path length formulation.

Path tracing bullet.

The Min-Path-Tracing method is the foundation of my thesis work. Interestingly, I first created this method during a student job in 2020, before my PhD even started, without knowing it was a novel approach.

The origin story.

MPT bullet.

The core challenge for differentiable RT is that visibility tests — checking whether a path is blocked — involve hard if-else conditions that break gradient flow. Our smoothing technique replaces these with continuous approximations.

Hard → smooth transition.

Smoothing bullet.

The smoothing technique was presented at EuCAP 2024 and has become my most cited work. It enables fully differentiable ray tracing, which we applied to antenna placement and material calibration.

Result figure placeholder.

Smoothing result bullet.

The smoothing technique has had a lasting impact: it is my most cited work and has been adopted by other groups. It also led to DiffeRT2d, an open-source library I built for teaching and rapid prototyping of differentiable RT.

DiffeRT2d card.

Impact bullet.

The second main contribution is about using machine learning for path tracing. While the optimization-based methods work well, they still require iterating for each path candidate. The idea here is to learn a model that directly predicts valid paths.

ML motivation bullet.

This contribution was born from a collaboration through the COST INTERACT action. I first visited Cesena in April 2024, and then spent four months in Bologna working with Prof. Vitucci and Prof. Degli-Esposti.

Collaboration map placeholder.

Collaboration bullet.

The ML architecture is a generative model: given the scene geometry and TX/RX positions, it predicts the interaction points for each path candidate. The model is trained on data generated from conventional RT.

Architecture block 1.

Architecture block 2.

Architecture block 3.

Architecture block 4.

Architecture block 5.

Architecture description bullet.

The model is trained on large-scale simulations. Each training sample consists of a scene configuration, TX/RX positions, and the ground-truth path coordinates computed by conventional RT.

Training/validation curves placeholder.

Training bullet.

The ML-based approach achieves significant speedups while maintaining accuracy comparable to conventional RT. This work was presented at ICMLCN 2025.

Results comparison placeholder.

ML result bullet.

The full journal version of this work was submitted to npj Wireless Technology in March 2026. It is the most comprehensive contribution of my thesis.

Journal bullet.

Key note about journal status.

The third and final contribution is the Fermat Path Tracing method, presented at EuCAP 2026. The key idea is a unified convex formulation that handles both reflection and diffraction using the same parametrization.

Annotated geometry / equation.

FPT setup bullet.

We use a BFGS quasi-Newton solver, which is well-suited for GPU execution because we fix the number of iterations to ensure uniform kernel execution.

BFGS bullet.

Why BFGS?

A key insight is the use of implicit differentiation. Instead of unrolling all solver iterations through the backward pass (which costs O(K) memory), we use the implicit function theorem at the converged solution.

Implicit diff bullet.

The implicit differentiation formula only requires the converged solution, not the full iteration history.

The FPT method was benchmarked against existing approaches. Our solver approaches the speed of the image method while supporting both reflections and diffractions in a unified framework.

Benchmark figure placeholder.

FPT result bullet.

All of these contributions are implemented in open-source software. DiffeRT is the full 3D library, while DiffeRT2d is a lightweight 2D version I created for prototyping and teaching.

Software cards.

Open source bullet.

Let me now summarize the three main contributions: the smoothing technique, the ML-based generative path tracing, and the Fermat Path Tracing method.

Plus cross-cutting contributions.

Beyond the scientific contributions, I am particularly proud of several achievements: building DiffeRT, the international collaborations, creating Manim Slides (which I am actually using right now to present these slides!), and contributing to the COST book.

Proud achievement bullet.

Looking ahead, several exciting research directions remain open. The main bottleneck remains the availability of efficient open GPU solvers.

Future direction bullet.

Key bottleneck warning.

Thank you all for your attention. I am happy to take your questions. The code, slides, and all related materials are available on GitHub.

Backup slide: other contributions not covered in the main presentation.

Other contribution bullet.

Backup slide: full list of publications during the PhD.