Phentax adapts black hole waveform calculations for LISA’s crowded signals

Why waveform calculations matter

The Laser Interferometer Space Antenna, or LISA, is a joint ESA–NASA space-based gravitational-wave detector that the paper describes as expected to launch in the mid-2030s. It will observe millihertz frequencies, a different range from current ground-based detectors.

Its expected sources include thousands of white dwarf binaries in our galaxy, compact objects spiraling into massive black holes, and massive black hole binaries with masses in the range of 10,000 to 10 million times the Sun’s mass.

Researchers are developing a strategy called a global fit: estimating the properties of many overlapping sources together. This can require hundreds of thousands of waveform templates—predictions of what a signal would look like for particular source properties. Generating those templates is a substantial computational task.

The same model, a different implementation

Phentax reimplements IMRPhenomTHM, an existing model that describes gravitational-wave signals as they evolve over time. It covers comparable-mass black hole binaries and includes higher-order modes: additional components of the signal beyond its dominant pattern.

The implementation is restricted to non-precessing binaries. It does not cover systems whose spin directions undergo precession. Users can calculate all supported modes or select a subset, and access individual signal components or the two gravitational-wave polarizations.

The software uses JAX, a numerical computing framework, to compile calculations and process batches of waveforms. Graphics processing units, or GPUs, can carry out many such calculations in parallel. Phentax also provides automatic derivatives, which describe how a predicted waveform changes when source parameters change. These can support inference methods that use gradients to explore possible parameter values.

The authors developed Phentax using the existing phenomxpy implementation as a guide. They report checking their waveforms against that implementation at several stages of development. The paper does not provide numerical error measures for those checks, so it does not establish a quantified agreement level in the supplied text.

Faster repeated calculations have a setup cost

JAX first traces and compiles a calculation, creating an initial warm-up cost. Changing an input’s shape or type can trigger compilation again.

To reduce that problem, Phentax reserves fixed-size arrays using a maximum observation duration. Different binaries can take different amounts of time to reach merger, so shorter signals leave unused space. The software pads unused waveform entries with zeros and returns a mask identifying valid samples.

The reported benchmarks examine both individual waveforms and batches on GPUs and CPUs. The individual-waveform timings exclude warm-up and use a six-month observation window, with averages over 50 realizations. The batching comparison uses a two-month window and shows warm-up separately.

The authors report that GPU batching takes advantage of parallel execution, whereas CPU batch times remain consistent with approximately linear growth as more waveforms are added. The GPU benchmarks used NVIDIA A100 hardware. These results should not be read as a universal speedup factor across machines, signal lengths or analysis pipelines.

An alternative to densely sampling every moment

Phentax also provides a time-frequency representation, which describes how a signal’s frequency content changes over time. Instead of first constructing a densely sampled time-domain waveform, it evaluates amplitudes and phases directly on a much sparser grid.

The authors identify this as particularly useful for lower-mass massive black hole binaries that remain in LISA’s frequency band for extended periods. One illustrated comparison shows an analytic time-frequency representation alongside a short Fourier transform of a time-domain signal. Its caption reports a runtime of about 150 microseconds for a signal of that length. That is an example-specific figure, not a timing for every waveform or a complete global fit.

What the preprint establishes—and what it does not

The software was developed around the simulated “Mojito Light” dataset, which contains 20 massive black hole binary signals alongside other LISA sources. The authors report adoption by global-fit pipelines in the LISA Distributed Data Processing Center and NASA Science Ground Segment, as well as searches and early-alert development efforts.

Those are uses in preparation for LISA, not detections or demonstrated alerts from real observations. The paper says results from the global-fit analyses are expected in future publications. It does not establish an end-to-end improvement in detection accuracy or source-parameter estimation.

Phentax is available through PyPI, with code on GitHub and accompanying documentation. This article draws on the supplied complete paper text, not only its abstract. The source is a preprint prepared for submission to the Journal of Open Source Software; peer-reviewed acceptance is not established by the supplied evidence.