<?xml-model href='http://www.tei-c.org/release/xml/tei/custom/schema/relaxng/tei_all.rng' schematypens='http://relaxng.org/ns/structure/1.0'?><TEI xmlns="http://www.tei-c.org/ns/1.0">
	<teiHeader>
		<fileDesc>
			<titleStmt><title level='a'>Robust Neural Network Approach to System Identificationin the High-Noise Regime</title></titleStmt>
			<publicationStmt>
				<publisher>Springer Verlag</publisher>
				<date>06/08/2023</date>
			</publicationStmt>
			<sourceDesc>
				<bibl> 
					<idno type="par_id">10519877</idno>
					<idno type="doi"></idno>
					
					<author>Elisa Negrini</author><author>Giovanna Citti</author><author>Luca Capogna</author>
				</bibl>
			</sourceDesc>
		</fileDesc>
		<profileDesc>
			<abstract><ab><![CDATA[We present a new algorithm for learning unknown gov- erning equations from trajectory data, using a family of neural net- works. Given samples of solutions x(t) to an unknown dynamical system x ̇ (t) = f (t, x(t)), we approximate the function f using a family of neural networks. We express the equation in integral form and use Euler method to predict the solution at every successive time step using at each iter- ation a different neural network as a prior for f. This procedure yields M-1 time-independent networks, where M is the number of time steps at which x(t) is observed. Finally, we obtain a single function f(t,x(t)) by neural network interpolation. Unlike our earlier work, where we numer- ically computed the derivatives of data, and used them as target in a Lipschitz regularized neural network to approximate f, our new method avoids numerical differentiations, which are unstable in presence of noise. We test the new algorithm on multiple examples in a high-noise setting. We empirically show that generalization and recovery of the governing equation improve by adding a Lipschitz regularization term in our loss function and that this method improves our previous one especially in the high-noise regime, when numerical differentiation provides low qual- ity target data. Finally, we compare our results with other state of the art methods for system identification.]]></ab></abstract>
		</profileDesc>
	</teiHeader>
	<text><body><div/></body></text>
</TEI>
