Introducing Heaviside-1

Electromagnetic design shapes the systems through which modern technology senses, communicates, and computes: from conformal antennas and phased arrays for spacecraft, to all-weather sensors for robots, to the packaging and high-speed interconnects inside advanced semiconductors. These systems are essential, but designing them remains slow, expensive, and dependent on scarce expert intuition.

At Arena Physica, our goal is to transform this process with a foundation model for electromagnetism (EM), a model trained not on language, but on electromagnetic fields and the geometries and materials that shape them. A model that develops a general understanding of how waves propagate, couple, reflect, and interfere across applications and, ultimately, across the electromagnetic spectrum from RF to photonics.

In March, we introduced Heaviside-0, our first step toward that goal. Today, we're introducing Heaviside-1: a major advance that expands from planar structures to fully 3D geometries and predicts full, complex electromagnetic vector fields in 3D.

The EM design loop

The typical design loop for an EM system is:

1. Specify the desired behavior (e.g. S-parameters, radiation patterns, etc.).
2. Design an initial geometry that might achieve the desired behavior.
3. Simulate the system to verify whether it matches the behavior.
4. Modify the design when it doesn't match the behavior.
5. Repeat steps 3 and 4 until the behavior is right.
6. Fabricate the design in the real world.
7. Measure with physical equipment to verify the behavior.
8. Repeat steps 2 through 7 until measured behavior matches target.

The design step, colloquially described as a "dark art" by most engineers, is driven by an RF engineer who built intuition over years (usually decades) to predict how electromagnetic systems will behave. The simulation step is performed by a sim expert (often, this is a different person altogether) who can navigate the intricacies of proprietary simulation software that is difficult to configure, expensive, and takes hours (often days) to run. Inevitably, the first simulation result doesn't match what the designer hoped to see, so the cycle starts over. This results in a design loop that is fragmented across experts and tools, expensive, and slow, even before fabrication begins.

Our launch of Atlas RF Studio in March showed how we can accelerate and simplify the EM design loop by pairing LLM-based agents with an EM foundation model.

Verification is the bottleneck

The slowest (pre-fabrication) step in the design loop is simulation. Full-wave field solvers like Ansys HFSS numerically compute a solution to Maxwell's equations over a discretized domain. This requires first constructing a "mesh" of the geometry (a challenging problem in itself, since a poorly constructed mesh can lead to inaccurate/non-convergent solutions), then brute-force solving a large system of partial differential equations until convergence criteria are met.

Design verification is what typically makes the design loop so hard to optimize, both for humans and for AI (see Verifier's rule). With a good verifier, AI systems can achieve superhuman performance. Games are obvious verifiers, resulting in feats like AlphaGo in 2016. Software engineering has unit tests, mathematics has formal theorem verification tools like Lean, letting AI "hill climb" to perfection. Electromagnetism doesn't have a good verifier. But if we could build one that is accurate, fast, and cheap, we could change that, unlocking superhuman AI for EM design.

Heaviside-0 already demonstrated speed: its deep neural network accelerated S-parameter calculation by up to 6 orders of magnitude compared to traditional field solvers. It did this by amortizing the brute-force simulation cost over millions of simulated training examples, encoding that experience into the model's learned latent space. That already proved to be powerful in a closed design loop, but its input design space was limited to 2.5D planar structures and its output was primarily restricted to S-parameters. And while it performed well in-distribution, it also wasn't as accurate as we wanted it to be on geometries far outside of the training distribution. To create a superhuman designer, we must first build a better verifier.

Since March, we have focused our efforts on creating a forward model that is more capable than the last and built to generalize. Enter Heaviside-1.

New capabilities: 3D geometries, 3D fields

Heaviside-1 is our latest forward model — 350M parameters (>10x the size of Heaviside-0, and roughly the same size as GPT-2), trained on 250k unique 3D field simulations (at 10k probe locations, 100 frequencies, and 2 ports per sim, that amounts to 500B total field samples, or >20 terabytes of data) — taking geometry, material properties, and excitation patterns as input, and predicting electromagnetic fields as output.

On the input side, we've overhauled the geometry encoder so that instead of 2.5D planar geometries (a stack of 2D images representing layers of patterned metal and dielectric), it now ingests fully 3D complex structures. For comparison, multimodal LLMs can't do this at all, since they are typically trained to ingest only words, audio, 2D images, and 2D video. Unlike Heaviside-1, no frontier LLM can handle arbitrary 3D geometry with invisible material properties like conductivity, permittivity, etc.

On the output side, we're now treating electric (E) and magnetic (H) near-fields as first-class prediction targets. Previously, Heaviside-0 trained primarily on S-parameters, but the full 3D vector fields encode much more information, letting the model learn a latent representation of the underlying physics vs. applied approximations used by most engineers. By doubling down on field-data generation and training, we were able to produce a model that generalizes significantly better to unseen geometry families than training on S-parameters alone. Plus, with near-fields as the primary target, we can begin to use the model to predict other downstream targets in the future (e.g. far-field radiation patterns).

We're particularly excited about Heaviside-1 because these two changes unlock a new family of industry use cases previously inaccessible to Heaviside-0. Fully 3D geometries allow us to describe essential structures in semiconductor packaging, conformal antennas for aviation and defense, and consumer applications like phones and wearables. Full EM vector field solutions provide a rich description that enables a wealth of downstream design-critical calculations (S-parameters, power flow, radiation patterns, signal integrity, etc.) and visual debugging capabilities in EM systems for RF/SIPI engineers.

To see Heaviside-1's capabilities in action, you can try Atlas Fields Studio, our interactive 3D field viewer (best viewed on a laptop/desktop computer). This lets you create a new geometry from a design template and explore how different shapes influence the E and H fields, in real time. What would normally take tens of minutes (if not hours) now takes milliseconds:

Here is just one example of a 3D geometry that Heaviside-1 can now predict fields for: a ball grid array (BGA), which is used to connect modern chips to PCBs, through spherical balls of solder. This matters because high-speed I/O for modern chips requires sending signals at hundreds of GHz, at which point you can't approximate a solder ball as a simple conductor, because it starts to behave more like a prism. The graphic below shows Heaviside-1's electric and magnetic field vector predictions at 10,000 probe locations around the structure:

Another challenging example shows the electric and magnetic fields plus the Poynting vector field lines of a hairpin bandpass filter at a frequency within its pass band, comparing ground truth from a simulator (left) to the Heaviside-1 prediction (right):

EMVal v1.0

Heaviside is a new class of foundation model, so there aren't any existing benchmarks we can borrow to evaluate performance.

To fill this gap, we're introducing EMVal v1.0, a new benchmark suite for evaluating EM foundation model capabilities. In its first iteration, the suite contains two tracks, EMVal-SP for S-parameter predictions, and EMVal-NF for near-field predictions in the time-harmonic domain. We maintain two private evaluation datasets, an in-distribution "standard" split and an out-of-distribution "challenge" split; none of these PCBs were seen during training, but out-of-distribution means that even the design templates that generated the PCBs in the dataset were excluded from training. We are also releasing a public version of the standard split for transparency, and so that the broader community can start to benchmark against it.

Today, these benchmarks focus on a limited set of geometries, board sizes, frequency ranges, material properties, and field probe distances. Over time, as we add more capabilities to Heaviside and improve overall model performance, we anticipate that we will saturate the v1.0 benchmarks and will need to graduate to a newer generation of benchmarks. To accommodate this progression, we will be releasing updated versions of EMVal that cover increasingly complex design spaces, as well as a new benchmark track, EMVal-FF, for far-field radiation predictions in the coming months.

EMVal-NF: Near-field

Heaviside-1 makes full 3D electromagnetic fields available for real-time design iteration. On geometry families represented during training, it predicts fields with ~19% global error and ~22% median local error; on entirely unseen families, those rise to ~33% and ~28% (which we will decrease in future releases by training on even more data). Predicted field direction and complex phase are highly faithful, with median vector alignment around 98%. This level of performance already makes Heaviside-1 useful for rapid exploration and debugging of designs — an engineer can trace coupling and energy flow, locate likely problem areas, and see the effect of a geometry change in milliseconds before committing time to a conventional simulation when they need production-level accuracy.

The chart below breaks out each metric by electric and magnetic field across the standard and challenge splits:

EMVal-SP: S-parameters

Full-field supervision is what enables Heaviside-1 to generalize. On familiar geometries, a model trained jointly on 3D fields and S-parameters performs about the same as one trained only on S-parameters. But on entirely unseen geometry families, the field-trained model performs substantially better. This supports our central hypothesis: learning the dense physical structure of electromagnetic fields produces a more general representation of EM than learning downstream quantities alone.

To isolate the effect of field supervision, we trained an otherwise identical version of Heaviside-1 with only one difference from our main model: instead of training on both fields and S-parameters, we trained it only on S-parameters. On in-distribution performance, both versions of Heaviside-1 perform similarly (~0.06 RMSE, ~0.45 dB mag-wMAE, ~0.09 phase-wMAE), and both beat Heaviside-0 by a substantial margin:

However, when we look at out-of-distribution (OOD) performance, we see a stark difference. Across the same metrics, Heaviside-1 trained only on S-parameters performs significantly worse than the jointly trained model. This demonstrates that the dense physical information contained within the complex 3D field distribution around the structure does in fact allow the model to generalize to completely unseen geometries far better than it does without it:

Looking forward

Heaviside-1 is an important step toward a true foundation model for electromagnetic design: one powerful model trained on electromagnetic structures and the fields they produce, which can support many downstream design tasks. Its ability to predict full 3D fields already, and to use that signal to generalize beyond familiar geometries, shows that this approach works.

As we move forward, we plan to continue scaling our geometric and material diversity, dataset size, and model size. To enable broader use cases, we are also adding support for more downstream physical targets, starting with far-field radiation patterns, extending Heaviside's prediction capability to the signals that matter most for antennas and wireless systems.

We're excited to keep pushing the frontier of electromagnetic superintelligence, and eager to hear your feedback on Heaviside-1. The best way to understand what it can already do is to interact with it yourself, so try out Atlas Fields Studio in beta (available on desktop) and let us know what you think. If you're a student interested in academic access and partnerships, please reach out to education@arenaphysica.com.