<p>There are actually some methods that could increase the accuracy of the model:</p>
<ol>
<li>Random Resampling</li>
<li>Residual Adaptive Refinement (RAR): <a href="https://arxiv.org/pdf/1907.04502.pdf" rel="nofollow noreferrer">https://arxiv.org/pdf/1907.04502.pdf</a></li>
</ol>
<p>They even have an implemented example in their github repository:</p>
<p><a href="https://github.com/lululxvi/deepxde/blob/master/examples/Burgers_RAR.py" rel="nofollow noreferrer">https://github.com/lululxvi/deepxde/blob/master/examples/Burgers_RAR.py</a></p>
<p>Also, You could try using a different architecture such as Multi-Scale Fourier NNs. They seem to outperform PINNs, in cases where the solution contains lots of &quot;spikes&quot;.</p>
Accuracy of solutions of differential equations with DeepXDE
<p>We used DeepXDE for solving differential equations. (DeepXDE is a framework for solving differential equations, based on TensorFlow). It works fine, but the accuracy of the solution is limited, and optimizing the meta-parameters did not help. Is this limitation a well-known problem? How the accuracy of solutions can be increased? We used the Adam-optimizer; are there optimizers that are more suitable for numerical problems, if high precision is needed?</p>
<p>(I think the problem is not specific for some concrete equation, but if needed I add an example.)</p>