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than roads?”
A: “0 (GT: 0)”
Aerial VHR Sentinel-2 Images
(a) (b)
FIGURE 4. The RSVQA system predictions for (a) Sentinel-2 and (b) aerial images, respectively, and different questions for each. The same
model is used to answer all of the questions related to one-resolution imagery. GT: ground truth; VHR: very high resolution. (Sources: (a)
Copernicus and (b) USGS.)
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JUNE 2021 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINEmodel can (and must) be improved: for example, au -
tomatic data generation has its flaws, especially due to
the very simplistic language model used, for which new
models from natural language processing could help im -
prove the performance greatly. Also, fewer classical tasks
(i.e., not reducible to classification, regression, or detec -
tion) should be imagined; for instance, when allowing for
more complex output spaces, the lessons learned from
image captioning in remote sensing [ 60] show that it is
possible to move toward models that generate descrip -
tions of the image content, which could be used in, e.g.,
image retrieval [ 61].
DIRECTION 4: PHYSICS-AWARE ML
As seen from the eyes of a practitioner, a major drawback
of deep learning models is that they can lead to implau -
sible results with scores that indicate high confidence
in the outputs if no high-level constraints are imposed
that check for consistency with theory. One possibility to
compensate for this shortcoming is integrating domain
knowledge into the modeling procedure. Particularly in
the environmental and geosciences, the laws of physics,
chemistry, or biology govern the underlying processes,
and much theory exists.
An interesting direction of research is thus how best
to tightly couple ML, and especially deep learning, with
physical laws. The hope is that this introduction of domain
knowledge can help reduce the manual labeling effort
for supervised learning, counter data set biases, lessen the
influence of label noise, lead to good generalization ca -
pabilities, and, eventually, result in plausible outputs that
adhere to the underlying physical principles. Machine
learning needs to incorporate domain physical knowledge
to become consistent, explainable (see direction 5 in Table 1),
and causal (see direction 6 in Table 1), while still learning
from observational data, which makes them amenable to
backpropagation. In addition, physics-consistent ML ap -
proaches for remote sensing emphasize modeling natural
phenomena with higher accuracy, which is not necessar -
ily the case for the two other research directions. In the
following sections, we present several ideas clustered into
three lines of thought: constrained optimization, physics
layers in deep neural networks, and encoding and learn -
ing differential equations. A recent overview of the main
families and approaches to the general field of the inter -
action between physics and ML for Earth observation is
available in [ 62].
CONSTRAINED OPTIMIZATION
A first consideration when designing physics-consistent ML
approaches is to impose constraints on the loss function
[13], [63]. Loss functions that encode the physical princi -
ples of a particular problem while using otherwise mostly
unchanged model architectures can ensure that the learned
model respects the laws of physics; see Figure 5 for an ex -
ample for including a dependence-based regularizer [ 52]. In addition, this strategy can significantly reduce the num -
ber of necessary labels required for training, down to prac -
tically zero in some cases [ 14].
Designing custom-tailored loss functions and possibly
combining them with models that are trained on simulat -
ed data represent another promising direction of research.
However, this approach calls for very specific designs of
loss functions that are not always straightforward and may
simply not exist for many problems in remote sensing. For
example, it seems very difficult to design a corresponding
loss function for the semantic segmentation of cars in aerial
images or the detection of building facades in street-level
panoramas because the large, intraclass variability of the ap -
pearances would require a very large set of constraints.
PHYSICS LAYERS IN DEEP NEURAL NETWORKS
An interesting idea, that of making use of well-established
deep neural networks but still learning and constraining
the underlying physics, is adding additional layers that
encode physics [ 1], [64] (see Figure 6 ). The general back -
ground knowledge gained from physics can be encoded
in the deeper network layers. Together with a custom-tailored
loss function, this approach enables the end-to-end
RMSE11.051.11.15NHSIC
0.264 0.266 0.268 0.27Morel1
CalCOFI
OC2
OC4
FIGURE 5. A standard family of hybrid modeling can be framed as
a constrained optimization problem, where the physical rules are
included as a particular form of regularizer [69]. The fair kernel learn -
ing [52] method forces model predictions to be not only accurate
but also statistically dependent on a physical model, simulations, or
ancillary observations. In this example, we forced the dependence
of a data-driven model with respect to four standard ocean-color
parametric models (Morel1, CalCOFI two-band linear, OC2, and OC4)
and trained our constrained model to estimate the levels of ocean
chlorophyll content from input radiances. We did so with increased
dependency (as estimated by the NHSIC metric) between the ML