diff --git a/src/meapy/heat_transfer.py b/src/meapy/heat_transfer.py
index 5f0147a..c6c4312 100644
--- a/src/meapy/heat_transfer.py
+++ b/src/meapy/heat_transfer.py
@@ -446,6 +446,15 @@ def analyse_exchanger(
     """
     if flow_direction not in {"counter", "co"}:
         raise ValueError(f"flow_direction must be 'counter' or 'co', got {flow_direction!r}.")
+    if math.isclose(t_mea_in_c, t_utility_in_c, abs_tol=1e-6):
+        # Without a driving force there is no hot/cold assignment, LMTD is
+        # undefined, and effectiveness divides by zero. Fail up front with a
+        # message that names the real cause rather than letting a downstream
+        # helper raise something cryptic.
+        raise ValueError(
+            f"t_mea_in_c ({t_mea_in_c}) and t_utility_in_c ({t_utility_in_c}) "
+            "are equal; no driving force, exchanger analysis is undefined."
+        )
 
     mea_kg_s = mea_flow_kg_h * _CONV
     util_kg_s = utility_flow_kg_h * _CONV
diff --git a/src/meapy/lambda_handler.py b/src/meapy/lambda_handler.py
index 087823f..e35cef0 100644
--- a/src/meapy/lambda_handler.py
+++ b/src/meapy/lambda_handler.py
@@ -64,6 +64,10 @@ def _analyse(body: JsonDict) -> JsonDict:
         result = heat_transfer.analyse_exchanger(**body)
     except TypeError as exc:
         return _response(400, {"error": f"bad payload: {exc}"})
+    except ValueError as exc:
+        # Physical/domain validation errors (e.g. non-positive flows, LMTD
+        # crossover) are caller-fixable inputs, not server faults.
+        return _response(400, {"error": f"invalid inputs: {exc}"})
     return _response(200, {"result": result})
 
 
diff --git a/src/meapy/pump.py b/src/meapy/pump.py
index d9174a7..b517aa7 100644
--- a/src/meapy/pump.py
+++ b/src/meapy/pump.py
@@ -106,6 +106,15 @@ def invert(self, target_level_pct: float) -> float:
         """
         if target_level_pct <= 0:
             raise ValueError(f"target_level_pct must be positive, got {target_level_pct!r}.")
+        if math.isclose(self.k, 0.0, abs_tol=1e-12):
+            # A flat fit (k = 0) means level is independent of speed; no
+            # finite speed solves L₀·exp(0) = target unless target == L₀,
+            # in which case every speed does. Either way, inversion is
+            # ill-posed — surface a clear error rather than dividing by zero.
+            raise ValueError(
+                "Cannot invert an ExponentialLevelModel with k ≈ 0: the fitted "
+                "level is independent of pump speed."
+            )
         return math.log(target_level_pct / self.l0) / self.k
 
 
@@ -246,6 +255,11 @@ def fit_exponential_level_model(
             f"All MEA level values must be strictly positive for log-linearisation.  "
             f"Found {(lev <= 0).sum()} non-positive value(s)."
         )
+    if np.ptp(ps) == 0:
+        raise ValueError(
+            "pump_speeds_pct has zero variance; cannot fit an exponential model "
+            "(slope would be undefined)."
+        )
 
     ln_lev = np.log(lev)
     slope, intercept, r, _, _ = linregress(ps, ln_lev)
@@ -284,6 +298,11 @@ def fit_linear_flowrate_model(
         )
     if len(ps) < 2:
         raise ValueError("At least 2 data points are required to fit a linear model.")
+    if np.ptp(ps) == 0:
+        raise ValueError(
+            "pump_speeds_pct has zero variance; cannot fit a linear model "
+            "(slope would be undefined)."
+        )
 
     slope, intercept, r, _, _ = linregress(ps, fl)
     r_sq = float(r**2)
diff --git a/src/meapy/utils.py b/src/meapy/utils.py
index 03cf0c8..9e4e9c4 100644
--- a/src/meapy/utils.py
+++ b/src/meapy/utils.py
@@ -184,6 +184,12 @@ def summarise_array(arr: npt.ArrayLike) -> dict[str, float]:
     a = np.asarray(arr, dtype=float).ravel()
     if a.size == 0:
         raise ValueError("Cannot summarise an empty array.")
+    if not np.all(np.isfinite(a)):
+        n_bad = int(np.sum(~np.isfinite(a)))
+        raise ValueError(
+            f"Input array contains {n_bad} non-finite value(s) (NaN/inf); "
+            "summary statistics would be poisoned. Clean or mask the data first."
+        )
     return {
         "mean": float(np.mean(a)),
         "std": float(np.std(a, ddof=1)) if a.size > 1 else 0.0,