AI models are widely perceived as black boxes: data goes in, an answer comes out, and the reasoning in between stays out of view. Our ability to build capable models has outpaced our ability to explain what happens inside them, which is why interpretability has become a field of its own, and why the case has been made that opaque models are unsuitable for high-stakes decisions.
This series aims to provide interpretability for the methods behind Physics AI: the strategies that go into building these models are unpacked and explained. Each article examines one part of how a model is put together, from how it reads a geometry to how it learns and predicts physical behavior. The goal is to make these methods understandable to the engineers who apply them in their design workflows.
When solving an engineering problem such as the flow over a wing, an engineer relies on known mathematical principles, including partial differential equations and shape functions, and on the physical laws that govern the problem. Because those principles are explicit, the engineer can make deliberate modeling choices, such as refining the mesh at the leading edge.
A Large Physics Model (LPM) applies machine learning to predict physical behavior from the shape of an object and its environment. It takes a geometry and a set of operating conditions as input and returns the resulting physical behavior. An LPM produces that prediction in seconds rather than the hours a solver would need, because it learns the mapping between inputs and outputs instead of solving the governing equations directly.
To learn that mapping, meaning how the shape of a wing affects the air flowing around it, the model has to “see” the features of the shape. Even something as simple as an edge has a very different effect on the flow depending on whether it is a leading edge or a trailing edge. This article describes the strategies LPMs use to perceive those features.
How a model reads a shape
In a simulation workflow, a solver reads a shape as a mesh: a discretization of the geometry into connected elements and volumes. The resolution of that discretization follows the complexity of the physics at each location rather than the shape itself, and it exists so that the solver can tractably solve the governing equations. An LPM works differently. It learns how shapes affect physics, so what matters is the form more than how individual elements connect to one another. Even so, a single point carries little information on its own. Its coordinates do not indicate whether it sits on a sharp leading edge or a broad flat panel. The model needs spatial context: information about the surrounding shape and about where the point sits on the body.
Several well-known approaches supply this context, and they differ in how they represent the shape. A signed distance function (SDF) replaces the surface with a field: for any point in space, it returns the distance to the nearest surface, signed negative inside the body and positive outside. Sampling that field near a point tells the model how close the surface is and which way it curves, without referring to any mesh. Other representations include voxel or occupancy grids, which resolve the shape onto a regular lattice, and graph-based encodings, which carry the connectivity of the surface mesh itself.
This article examines two approaches in detail. The first gathers neighboring points from the geometry. The second encodes position as a spectrum of frequencies.
Approach 1: Gather Neighboring Points
The first approach measures the geometry directly. For each point, the model collects the neighboring points within a given radius and repeats this at several radii, from small to large.
Each radius contributes something different. A fine radius captures local shape, such as the curvature at a leading edge. A coarse radius captures location, such as the region of the body the point belongs to. The model needs both the local detail and the broader placement.
Because neighbors are gathered by distance in physical space rather than by traversing a mesh, the resulting context does not depend on how elements connect to one another, though it does depend on how densely the surface is sampled. What this produces is geometric context, meaning what the surface is doing around a point, rather than a precise account of where that point sits, so models that gather neighbors still encode the coordinates themselves.
Gathering introduces additional runtime cost: neighborhoods are constructed across the full set of sampled surface locations, the point cloud, at every radius, each time the model produces a prediction.
GeoTransolver implements this strategy through multi-scale ball queries.
Approach 2: Encode Position as a Spectrum
The second mechanism works on the coordinates themselves rather than on the surrounding geometry. It converts each coordinate into a richer input feature.
Raw coordinates work poorly here because of how neural networks learn. A network fed raw coordinates is biased toward smooth functions: it represents a gradual pressure gradient easily and sharp features poorly. For example, consider the suction peak on a wing: it varies over a few percent of chord and is hard to build from three smoothly varying inputs, and doing so demands substantial network depth and training.
The solution is to encode each coordinate as a set of sine and cosine functions across many frequencies. Low frequencies vary slowly and distinguish points coarsely. High frequencies vary quickly and distinguish points that sit close together. With these functions available, a sharp feature becomes a linear combination of existing features rather than a function that the network must construct.
Increasing the number of frequency bands brings the suction peak into focus. With the raw coordinate alone, the best fit is close to a straight line. Low-frequency bands recover the broad shape but leave the peak too wide. The peak sharpens when the highest available frequency approaches the scale of the feature.
This technique is positional encoding. The frequency content of the encoding strongly influences the spatial scales the model can readily distinguish and learn, so the set of frequencies is chosen deliberately.
Trade-offs
The two mechanisms address different problems. Neighbor gathering supplies geometric context: what the surface is doing around a point, across several scales. Frequency encoding changes how position is presented to the network, so that variation over short distances becomes easier to learn.
Their costs also differ in kind. Neighbor gathering adds work at every radius, each time the model runs. Frequency encoding costs little by comparison; its highest band sets the fastest variation the encoding itself contains, which is why the frequency range is chosen against the scale of the features that matter. Some models extend the technique with a modulated encoding, which varies the emphasis across frequencies by region.
These approaches are not mutually exclusive: a model can gather neighbors, encode position as frequencies, and read an SDF field at the same time, and several architectures combine more than one so that each supplies the kind of spatial information it represents best.
This is what a Physics AI model sees. The next article describes what the model does with these inputs and what it learns.
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