  We model acoustic dynamics in space and time from synthetic sensor data. The
tasks are (i) to predict and extrapolate the spatiotemporal dynamics, and (ii)
reconstruct the acoustic state from partial observations. To achieve this, we
develop acoustic neural networks that learn from sensor data, whilst being
constrained by prior knowledge on acoustic and wave physics by both informing
the training and constraining parts of the network's architecture as an
inductive bias. First, we show that standard feedforward neural networks are
unable to extrapolate in time, even in the simplest case of periodic
oscillations. Second, we constrain the prior knowledge on acoustics in
increasingly effective ways by (i) employing periodic activations (periodically
activated neural networks); (ii) informing the training of the networks with a
penalty term that favours solutions that fulfil the governing equations
(soft-constrained); (iii) constraining the architecture in a
physically-motivated solution space (hard-constrained); and (iv) combination of
these. Third, we apply the networks on two testcases for two tasks in nonlinear
regimes, from periodic to chaotic oscillations. The first testcase is a twin
experiment, in which the data is produced by a prototypical time-delayed model.
In the second testcase, the data is generated by a higher-fidelity model with
mean-flow effects and a kinematic model for the flame source. We find that (i)
constraining the physics in the architecture improves interpolation whilst
requiring smaller network sizes, (ii) extrapolation in time is achieved by
periodic activations, and (iii) velocity can be reconstructed accurately from
only pressure measurements with a combination of physics-based hard and soft
constraints. In and beyond acoustics, this work opens strategies for
constraining the physics in the architecture, rather than the training.
