  We simulate lattice QCD at finite quark-number chemical potential to study
nuclear matter, using the complex Langevin equation (CLE). The CLE is used
because the fermion determinant is complex so that standard methods relying on
importance sampling fail. Adaptive methods and gauge-cooling are used to
prevent runaway solutions. Even then, the CLE is not guaranteed to give correct
results. We are therefore performing extensive testing to determine under what,
if any, conditions we can achieve reliable results. Our earlier simulations at
$\beta=6/g^2=5.6$, $m=0.025$ on a $12^4$ lattice reproduced the expected phase
structure but failed in the details. Our current simulations at $\beta=5.7$ on
a $16^4$ lattice fail in similar ways while showing some improvement. We are
therefore moving to even weaker couplings to see if the CLE might produce the
correct results in the continuum (weak-coupling) limit, or, if it still fails,
whether it might reproduce the results of the phase-quenched theory. We also
discuss action (and other dynamics) modifications which might improve the
performance of the CLE.
