Abstract
The deep operator network (DeepONet) architecture is a promising
approach for learning functional operators, that can represent dynamical
systems described by ordinary or partial differential equations.
However, it has two major limitations, namely its failures to account
for initial conditions and to guarantee the temporal causality – a
fundamental property of dynamical systems. This paper proposes a novel
causal deep operator network (Causal-DeepONet) architecture for
incorporating both the initial condition and the temporal causality into
data-driven learning of dynamical systems, overcoming the limitations of
the original DeepONet approach. This is achieved by adding an
independent root network for the initial condition and independent
branch networks conditioned, or switched on/off, by time-shifted step
functions or sigmoid functions for expressing the temporal causality.
The proposed architecture was evaluated and compared with two baseline
deep neural network methods and the original DeepONet method on learning
the thermal dynamics of a room in a building using real data. It was
shown to not only achieve the best overall prediction accuracy but also
enhance substantially the accuracy consistency in multistep predictions,
which is crucial for predictive contro